eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
1
13
10.22108/toc.2017.21472
21472
The central vertices and radius of the regular graph of ideals
Farzad Shaveisi
f.shaveisi@ipm.ir
1
Razi University
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.
http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf
Arc
artinian ring
eccentricity
radius
regular digraph
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
15
27
10.22108/toc.2017.21471
21471
The harmonic index of subdivision graphs
Bibi Naimeh Onagh
bn.onagh@gu.ac.ir
1
Golestan University
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.
http://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf
harmonic index
subdivision
$S$-sum
inverse degree
Zagreb index
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
29
42
10.22108/toc.2017.21614
21614
Splices, Links, and their Edge-Degree Distances
Mahdieh Azari
mahdie.azari@gmail.com
1
Hojjatollah Divanpour
h.divanpour@yahoo.com
2
Kazerun Branch, Islamic Azad University
Shiraz Technical College, Technical and Vocational University
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.
http://toc.ui.ac.ir/article_21614_033f4714ff9a47c358a450a46e9a3122.pdf
Distance
degree
edge-degree distance
splice of graphs
link of graphs
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
43
50
10.22108/toc.2017.21470
21470
On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph
Hanyuan Deng
hydeng@hunnu.edu.cn
1
S. Balachandran
bala@maths.sastra.edu
2
S. K. Ayyaswamy
3
Y. B. Venkatakrishnan
venkatakrish2@maths.sastra.edu
4
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
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}.
http://toc.ui.ac.ir/article_21470_6107bccf810358fdefb9471c7d0ba0a8.pdf
Average eccentricity
harmonic index
signless Laplacian eigenvalue
extremal value
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
51
65
10.22108/toc.2017.21467
21467
Some topological indices and graph properties
Xiaomin Zhu
962186133@qq.com
1
Lihua Feng
fenglh@163.com
2
Minmin Liu
903069441@qq.com
3
Weijun Liu
wjliu6210@126.com
4
Yuqin Hu
1120233887@qq.com
5
College of Science, Nantong University, Nantong, China
School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China.
School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China.
School of Science, Nantong University, Nantong,226019， China,
School of Mathematics and Statistics, Central South University New Campus, Changsha, Hunan, China.
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.
http://toc.ui.ac.ir/article_21467_d05e2410fc3d5c5560f3430866b8af0e.pdf
Topological indices
degree sequences
graph properties