Browsing by Author "CANGÜL, İSMAİL NACİ"
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Publication A presentation and some finiteness conditions for a new version of the schiitzenberger product of monoids(Tübitak Bilimsel ve Teknolojik Araştırma Kurumu, 2016-01-01) Karpuz, Eylem Güzel; Ateş, Firat; Cevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7111-3462; 0000-0002-0700-5774; ABA-6206-2020In this paper we first define a new version of the Schutzenberger product for any two monoids A and B, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.Publication An explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNC k (n)(Analytic Publ Co, 2020-01-01) Sardar, Muhammad Shoaib; Xu, Si-Ao; Sajjad, Wasim; Zafar, Sohail; Cangül, İsmail Naci; Farahani, Mohammad R.; CANGÜL, İSMAİL NACİ; 0000-0002-0700-5774; J-3505-2017Let G be a simple molecular graph without directed and multiple edges and without loops. The vertex and edge-sets of G are denoted by V(G) and E(G), respectively. Suppose G is also a connected molecular graph and let u, v is an element of V(G) be two vertices. The harmonic index H(G) of G is defined as the sum of the weights 2(d(u)+d(v))(-1) of all edges in E(G), where d(v) is the degree of a vertex v in G which is defined as the number of vertices of G adjacent to v. The harmonic polynomial of G is defined as H(G, x) = Sigma(e=uv is an element of E(G)) 2x((du+dv-1)) and there is the following nice relation between these two notions H(G) = integral(1)(0) H(G, x)dx. In this paper, we present an explicit formula for the harmonic indices and harmonic polynomials of carbon nanocones CNCk[n].Publication Bounds for the sum of cubes of vertex degrees of splice graphs(Turkic World Mathematical, 2020-01-01) Lokesha, Veerebradiah; Jain, Sushmitha; Muddalapuram, Manjunath; Çevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017Some chemically interesting graphs can be derived from simpler graphs by some graph operations. One of the most relevant among these interesting graphs is named as splice graphs. They are related to RNA sequencing and therefore is of great interest. The main target of this paper is to obtain the explicit interpretation of F-index in terms of the graph size and maximum or minimum vertex degrees of special splice graphs.Publication Computing the hosoya and the merrifield-simmons indices of two special benzenoid systems(Univ Kashan, Fac Mathematical Sciences, 2021-06-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; J-3505-2017Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems R-n and P-n. In this paper, we compute the Hosoya index and Merrifield-Simmons index of R-n and P-n, by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of R-n and P-n, by means of a product of a certain matrix of degree n and a certain vector.Publication Computing the Merrifield-Simmons indices of benzenoid chains and double benzenoid chains(Springer Heidelberg, 2022-10) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017In this paper, we introduce the Merrifield-Simmons vector defined at a path of corresponding double hexagonal (benzenoid) chain. By utilizing this vector, we present reduction formulae to compute the Merrifield-Simmons index sigma(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute sigma(H) of H by means of a product of some of obtained six matrices and a vector with entries in N. Subsequently, we introduce the simple Merrifield-Simmons vector defined at an edge of given graph G. By using simple Merrifield-Simmons vector we present reduction formulae to compute the sigma(G) where G represents any hexagonal (benzenoid) chain.Publication Distance eccentric connectivity index of graphs(Kyungpook Natl Univ, Dept Mathematics, 2021-03-01) Alqesmah, Akram; Saleh, Anwar; Rangarajan, R.; Gunes, Aysun Yurttas; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-6251-5518; 0000-0002-0700-5774; AAG-8470-2021; AGP-4352-2022; J-3505-2017; ACA-0773-2022Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by xi(C) (G) = Sigma(u)(is an element of V)((G)) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of xi(C) that will be called the distance eccentric connectivity index of G and defined byxi(De)(G) = Sigma(u is an element of V(G))deg(De)(u)e(u)where deg(De)(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.Publication Edge-zagreb indices of graphs(Turkic World Mathematical Soc, 2020-01-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Yamaç, Çilem; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017The algebraic study of graph matrices is an important area of Graph Theory giving information about the chemical and physical properties of the corresponding molecular structure. In this paper, we deal with the edge-Zagreb matrices defined by means of Zagreb indices which are the most frequently used graph indices.Publication Effect of edge and vertex addition on albertson and bell indices(Amer Inst Mathematical Sciences-aims, 2021-01-01) Delen, Sadık; Cangül, İsmail Naci; Delen, Sadık; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017; EUU-3205-2022Topological graph indices have been of great interest in the research of several properties of chemical substances as it is possible to obtain these properties only by using mathematical calculations. The irregularity indices are the ones to determine the degree of irregularity of a graph. Albertson and Bell indices are two of them. Edge and vertex deletion and addition are important and useful methods in calculating several properties of a given graph. In this paper, the effects of adding a new edge or a new vertex to a graph on the Albertson and Bell indices are determined.Publication Encrypting and decrypting algorithms using strong face graph of a tree(Taylor & Francis Ltd, 2020-10-01) Kuppan, R.; Shobana, L.; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; 0000-0002-6401-6533; 0000-0002-0700-5774; ABE-7781-2021; J-3505-2017The encryption and decryption is based upon the type of cryptographic scheme being employed and also in some form of key. It is most closely associated with the development and creation of the mathematical algorithms used to encrypt and decrypt messages. The combination of graph labelling techniques together with cryptography to encrypt and decrypt the numbers has been already an ongoing aspect of research. In this paper, the concept of face antimagic labelling is used for a strong face of duplication of all vertices by the edges of a tree to encrypt and decrypt 13 secret numbers.Publication Harmonic index and zagreb indices of vertex-semitotal graphs(New York Business Global Llc, 2020-01-01) Günes, Aysun Yurttaş; YURTTAŞ GÜNEŞ, AYSUN; Togan, Muge; Demirci, Musa; DEMİRCİ, MUSA; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant.Publication Independence number of graphs and line graphs of trees by means of omega invariant(Springer, 2020-02-26) Srivastava, Gautam; Srivastava, Hari Mohan; Ozden, Hacer; ÖZDEN AYNA, HACER; Zihni, Fikriye Ersoy; Erdogan, Fatma Ozen; ÖZEN ERDOĞAN, FATMA; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-3991-0488; AAH-5090-2021; ABA-6206-2020; J-3505-2017; AAG-8274-2021A recently defined graph invariant denoted by O(G) for a graph G is shown to have several applications in graph theory. This number gives direct information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges, etc. In this paper, we use O to give a characterization of connected unicyclic graphs, to calculate the omega invariant and to formalize the number of faces of the line graph of a tree, and give a new algorithm to formalize the independence number of graphs G and line graphs L(G) by means of the support vertices, pendant vertices and isolated vertices in G.Publication Inverse problem for bell index(Univ Nis, Fac Sci Math, 2020-01-01) Togan, Müge; Yurttaş, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Şanlı, Utkum; Çelik, Feriha; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5349-3978; 0000-0002-0700-5774; J-3505-2017; AAG-8470-2021Due to their applications in many branches of science, topological graph indices are becoming more popular every day. Especially as one can model chemical molecules by graphs to obtain valuable information about the molecules using solely mathematical calculations on the graph. The inverse problem for topological graph indices is a recent problem proposed by Gutman and is about the existence of a graph having its index value equal to a given non-negative integer. In this paper, the inverse problem for Bell index which is one of the irregularity indices is solved. Also a recently defined graph invariant called omega invariant is used to obtain several properties related to the Bell index.Publication Matching number and characteristic polynomial of a graph(Taylor & Francis, 2020-07-11) Yurttaş Güneş, Aysun; Demirci, Musa; Öz, Mert Sinan; Cangül, İsmail Naci; YURTTAŞ GÜNEŞ, AYSUN; DEMİRCİ, MUSA; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-6439-8439; AAG-8470-2021; A-6557-2018; J-3505-2017Matching number and the spectral properties depending on the characteristic polynomial of a graph obtained by means of the adjacency polynomial has many interesting applications in different areas of science. There are some work giving the relation of these two areas. Here the relations between these two notions are considered and several general results giving this relations are obtained. A result given for only unicyclic graphs is generalized. There are some methods for determining the matching number of a graph in literature. Usually nullity, spanning trees and several graph parts are used to do this. Here, as a new method, the conditions for calculating the matching number of a graph by means of the coefficients of the characteristic polynomial of the graph are determined. Finally some results on the matching number of graphs are obtained.Publication Omega index of line and total graphs(Hindawi, 2021-09-09) Demirci, Musa; Delen, Sadık; Çevik, Ahmet Sinan; Cangül, İsmail Naci; DEMİRCİ, MUSA; Delen, Sadık; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-6439-8439; 0000-0003-4689-3660; 0000-0002-0700-5774; A-6557-2018; EUU-3205-2022 ; J-3505-2017A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.Publication On L(h, k)-labeling index of inverse graphs associated with finite cyclic groups(Hindawi, 2021-03-11) Mageshwaran, K.; Kalaimurugan, G.; Hammachukiattikul, Bussakorn; Govindan, Vediyappan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017An L(h, k)-labeling of a graph G. (V, E) is a function f: V -> [0,8) such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between the vertices separated by a distance 2 is at least k. *e difference between the highest and lowest assigned values is the index of an L(h, k)-labeling. The minimum number for which the graph admits an L(h, k)-labeling is called the required possible index of L(h, k)-labeling of G, and it is denoted by lambda(h)(k) (G). In this paper, we obtain an upper bound for the index of the L(h, k)-labeling for an inverse graph associated with a finite cyclic group, and we also establish the fact that the upper bound is sharp. Finally, we investigate a relation between L(h, k)-labeling with radio labeling of an inverse graph associated with a finite cyclic group.Publication On omega index and average degree of graphs(Hindawi, 2021-11-12) Delen, Sadık; Demirci, Musa; Cevik, Ahmet Sinan; Cangül, İsmail Naci; Delen, Sadık; DEMİRCİ, MUSA; CANGÜL, İSMAİL NACİ; 0000-0002-0700-5774; 0000-0002-6439-8439; 0000-0003-4689-3660; A-6557-2018; J-3505-2017; EUU-3205-2022Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determined and a new proof of the handshaking lemma has been given. Using a recently defined graph index called omega index, average degree of trees, unicyclic, bicyclic, and tricyclic graphs have been given, and these have been generalized to k-cyclic graphs. Also, the effect of edge deletion has been calculated. The average degree of some derived graphs and some graph operations have been determined.Publication Some graph parameters of power set graphs(Pushpa Publishing House, 2021-03-01) Nacaroğlu, Yaşar; Akgüneş, Nihat; Pak, Sedat; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; J-3505-2017In this study, we examine some graph parameters such as the edge number, chromatic number, girth, domination number and clique number of power set graphs.Publication Some inequalities for the first general zagreb index of graphs and line graphs(Natl Acad Sciences India, 2020-04-02) Chaluvaraju, B.; Boregowda, H. S.; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020The first general Zagreb index M1 alpha(G) of a graph G is equal to the sum of the alpha th powers of the vertex degrees of G. For alpha >= 0 and k >= 1, we obtain the lower and upper bounds for M1 alpha(G) and M1 alpha(L(G)) in terms of order, size, minimum/maximum vertex degrees and minimal non-pendant vertex degree using some classical inequalities and majorization technique, where L(G) is the line graph of G. Also, we obtain some bounds and exact values of M1 alpha(J(G)) and M1 alpha(Lk(G)), where J(G) is a jump graph (complement of a line graph) and Lk(G) is an iterated line graph of a graph G.Publication Sum-edge characteristic polynomials of graphs(Taylor & Francis, 2019-01-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Yamaç, Çilem; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; ABA-6206-2020Modelling a chemical compound by a (molecular) graph helps us to obtain some required information about the chemical and physical properties of the corresponding molecular structure. Linear algebraic notions and methods are used to obtain several properties of graphs usually by the help of some graph matrices and these studies form an important sub area of Graph Theory called spectral graph theory. In this paper, we deal with the sum-edge matrices defined by means of vertex degrees. We calculate the sum-edge characteristic polynomials of several important graph classes by means of the corresponding sum-edge matrices.Publication The effect of edge and vertex deletion on omega invariant(Univ Belgrade, Fac Electrical Engineering, 2020-12-01) Delen, Sadık; Togan, Müge; Yurttaş, Aysun; Ana, Uğur; Cangül, İsmail Naci; Delen, Sadık; Togan, Müge; YURTTAŞ GÜNEŞ, AYSUN; Ana, Uğur; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0001-5349-3978; 0000-0002-0700-5774; AAG-8470-2021; J-3505-2017; EUU-3205-2022; GBL-2333-2022; CBI-5098-2022Recently the first and last authors defined a new graph characteristic called omega related to Euler characteristic to determine several topological and combinatorial properties of a given graph. This new characteristic is defined in terms of a given degree sequence as a graph invariant and gives a lot of information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges etc. of the family of realizations.In this paper, the effect of the deletion of vertices and edges from a graph on omega invariant is studied.