University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
4
2017
12
01
The central vertices and radius of the regular graph of ideals
1
13
EN
Farzad
Shaveisi
Razi University
f.shaveisi@ipm.ir
10.22108/toc.2017.21472
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.
Arc,artinian ring,eccentricity,radius,regular digraph
http://toc.ui.ac.ir/article_21472.html
http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
4
2017
12
01
The harmonic index of subdivision graphs
15
27
EN
Bibi Naimeh
Onagh
Golestan University
bn.onagh@gu.ac.ir
10.22108/toc.2017.21471
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.
harmonic index,subdivision,$S$-sum,inverse degree,Zagreb index
http://toc.ui.ac.ir/article_21471.html
http://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
4
2017
12
01
Splices, Links, and their Edge-Degree Distances
29
42
EN
Mahdieh
Azari
Kazerun Branch, Islamic Azad University
mahdie.azari@gmail.com
Hojjatollah
Divanpour
Shiraz Technical College, Technical and Vocational University
h.divanpour@yahoo.com
10.22108/toc.2017.21614
The edge-degree distance of a simple connected graph G is defined as the sum of the terms (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 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.
Distance,degree,edge-degree distance,splice of graphs,link of graphs
http://toc.ui.ac.ir/article_21614.html
http://toc.ui.ac.ir/article_21614_033f4714ff9a47c358a450a46e9a3122.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
4
2017
12
01
On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph
43
50
EN
Hanyuan
Deng
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China
hydeng@hunnu.edu.cn
S.
Balachandran
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
bala@maths.sastra.edu
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
venkatakrish2@maths.sastra.edu
10.22108/toc.2017.21470
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}.
Average eccentricity,harmonic index,signless Laplacian eigenvalue,extremal value
http://toc.ui.ac.ir/article_21470.html
http://toc.ui.ac.ir/article_21470_6107bccf810358fdefb9471c7d0ba0a8.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
4
2017
12
01
Some topological indices and graph properties
51
65
EN
Xiaomin
Zhu
College of Science, Nantong University, Nantong, China
962186133@qq.com
Lihua
Feng
School of Mathematics and Statistics, Central South University
New Campus, Changsha, Hunan, China.
fenglh@163.com
Minmin
Liu
School of Mathematics and Statistics, Central South University
New Campus, Changsha, Hunan, China.
903069441@qq.com
Weijun
Liu
School of Science, Nantong University, Nantong,226019， China,
wjliu6210@126.com
Yuqin
Hu
School of Mathematics and Statistics, Central South University
New Campus, Changsha, Hunan, China.
1120233887@qq.com
10.22108/toc.2017.21467
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.
Topological indices,degree sequences,graph properties
http://toc.ui.ac.ir/article_21467.html
http://toc.ui.ac.ir/article_21467_d05e2410fc3d5c5560f3430866b8af0e.pdf