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
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
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
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