eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2017-12-01
6
4
1
13
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
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
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