University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 The central vertices and radius of the regular graph of ideals‎ 1 13 21472 10.22108/toc.2017.21472 EN Farzad Shaveisi Razi University Journal Article 2016 10 17 The regular graph of ideals of the commutative ring \$R\$‎, ‎denoted by \${Gamma_{reg}}(R)\$‎, ‎is a graph whose vertex‎ ‎set is the set of all non-trivial ideals of \$R\$ and two distinct vertices \$I\$ and \$J\$ are adjacent if and only if either \$I\$ contains a \$J\$-regular element or \$J\$ contains an \$I\$-regular element‎. ‎In this paper‎, ‎it is proved that the radius of \$Gamma_{reg}(R)\$ equals \$3\$‎. ‎The central vertices of \$Gamma_{reg}(R)\$ are determined‎, ‎too‎. https://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf
University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 The harmonic index of subdivision graphs 15 27 21471 10.22108/toc.2017.21471 EN Bibi Naimeh Onagh Golestan University Journal Article 2016 09 07 ‎The harmonic index of a graph \$G\$ is defined as the sum of the weights‎ ‎\$frac{2}{deg_G(u)+deg_G(v)}\$ of all edges \$uv\$‎ ‎of \$G\$‎, ‎where \$deg_G(u)\$ denotes the degree of a vertex \$u\$ in \$G\$‎. ‎In this paper‎, ‎we study the harmonic index of subdivision graphs‎, ‎\$t\$-subdivision graphs and also‎, ‎\$S\$-sum and \$S_t\$-sum of graphs‎. https://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf
University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 Splices, Links, and their Edge-Degree Distances 29 42 21614 10.22108/toc.2017.21614 EN Mahdieh Azari Kazerun Branch, Islamic Azad University Hojjatollah Divanpour Shiraz Technical College, Technical and Vocational University Journal Article 2017 01 28 The edge-degree distance of a simple connected graph G is defined as the sum of the terms<br /> (d(e|G)+d(f|G))d(e,f|G) over all unordered pairs {e,f} of edges of G, where d(e|G) and<br /> d(e,f|G) denote the degree of the edge e in G and the distance between the edges e and f in G, respectively. In this paper, we study the behavior of two versions of the edge-degree distance under two graph products called splice and link. https://toc.ui.ac.ir/article_21614_033f4714ff9a47c358a450a46e9a3122.pdf
University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 On the average eccentricity‎, ‎the harmonic index and the largest signless Laplacian eigenvalue of a graph 43 50 21470 10.22108/toc.2017.21470 EN Hanyuan Deng College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China S. Balachandran Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India ‎S. K. Ayyaswamy Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India Y. B. Venkatakrishnan Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India Journal Article 2017 03 08 The eccentricity of a vertex is the maximum distance from it to‎ ‎another vertex and the average eccentricity \$eccleft(Gright)\$ of a‎ ‎graph \$G\$ is the mean value of eccentricities of all vertices of‎ ‎\$G\$‎. ‎The harmonic index \$Hleft(Gright)\$ of a graph \$G\$ is defined‎ ‎as the sum of \$frac{2}{d_{i}+d_{j}}\$ over all edges \$v_{i}v_{j}\$ of‎ ‎\$G\$‎, ‎where \$d_{i}\$ denotes the degree of a vertex \$v_{i}\$ in \$G\$‎. ‎In‎ ‎this paper‎, ‎we determine the unique tree with minimum average‎ ‎eccentricity among the set of trees with given number of pendent‎ ‎vertices and determine the unique tree with maximum average‎ ‎eccentricity among the set of \$n\$-vertex trees with two adjacent‎ ‎vertices of maximum degree \$Delta\$‎, ‎where \$ngeq 2Delta\$‎. ‎Also‎, ‎we‎ ‎give some relations between the average eccentricity‎, ‎the harmonic‎ ‎index and the largest signless Laplacian eigenvalue‎, ‎and strengthen‎ ‎a result on the Randi'{c} index and the largest signless Laplacian‎ ‎eigenvalue conjectured by Hansen and Lucas cite{hl}‎. https://toc.ui.ac.ir/article_21470_6107bccf810358fdefb9471c7d0ba0a8.pdf
University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 Some topological indices and graph properties 51 65 21467 10.22108/toc.2017.21467 EN Xiaomin Zhu College of Science, Nantong University, Nantong, China Lihua Feng School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China. Minmin Liu School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China. Weijun Liu School of Science, Nantong University, Nantong,226019， China, Yuqin Hu School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China. Journal Article 2016 06 12 In this paper, by using the degree sequences of graphs, we present sufficient conditions for a graph to be Hamiltonian, traceable, Hamilton-connected or \$k\$-connected in light of numerous topological indices such as the eccentric connectivity index, the eccentric distance sum, the connective eccentricity index. https://toc.ui.ac.ir/article_21467_d05e2410fc3d5c5560f3430866b8af0e.pdf