Browsing by Author "Gutman, Ivan"
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Item Inverse problem for sigma index(University of Kragujevac, 2018) Gutman, Ivan; Çevik, Ahmet Sinan; Togan, Müge; Yurttaş, Aysun; Naci Cangül, İsmail; Uludağ Üniversitesi/Fen - Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; GBL-2333-2022; AAG-8470-2021; J-3505-2017; 54403978300; 37090056000; 57189022403If G is a (molecular) graph and d(v), the degree of its vertex u, then its sigma index is defined as sigma(G) = Sigma(d(u) - d(v))(2), with summation going over all pairs of adjacent vertices. Some basic properties of sigma(G) are established. The inverse problem for topological indices is about the existence of a graph having its index value equal to a given non-negative integer. We study the problem for the sigma index and first show that sigma(G) is an even integer. Then we construct graph classes in which sigma(G) covers all positive even integers. We also study the inverse problem for acyclic, unicyclic, and bicyclic graphs.Item Inverse problem for Zagreb indices(Springer, 2018-10-23) Lokesha, Veerebradiah; Gutman, Ivan; Yurttaş, Aysun; Togan, Müge; Cangül, İsmail Naci; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; AAG-8470-2021; 57204472437; 54403978300; 57189022403The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.