Browsing by Author "Cangul, Ismail Naci"
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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 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 On the wiener index of the dot product graph over monogenic semigroups(New York Business Global Llc, 2020-01-01) Aydin, Busra; Akgunes, Nihat; Cangul, Ismail Naci; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; J-3505-2017Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the finite dot product of monogenic semigroups has recently been defined and in this paper, some results on the Wiener index of the dot product graph over monogenic semigroups are given.