Browsing by Author "Alqesmah, Akram"

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    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-0773-2022
    Let 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.
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    Publication
    Entire zagreb indices of graphs
    (World Scientific Publ Co Pte Ltd, 2018-06-01) Alwardi, Anwar; Alqesmah, Akram; Rangarajan, R.; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Eğitim Fakültesi; 0000-0002-0700-5774; J-3505-2017; ABA-6206-2020
    The Zagreb indices have been introduced in 1972 to explain some properties of chemical compounds at molecular level mathematically. Since then, the Zagreb indices have been studied extensively due to their ease of calculation and their numerous applications in place of the existing chemical methods which needed more time and increased the costs. Many new kinds of Zagreb indices are recently introduced for several similar reasons. In this paper, we introduce the entire Zagreb indices by adding incidency of edges and vertices to the adjacency of the vertices. Our motivation in doing so was the following fact about molecular graphs: The intermolecular forces do not only exist between the atoms, but also between the atoms and bonds, so one should also take into account the relations (forces) between edges and vertices in addition to the relations between vertices to obtain better approximations to intermolecular forces. Exact values of these indices for some families of graphs are obtained and some important properties of the entire Zagreb indices are established.