2017
6
4
4
0
The central vertices and radius of the regular graph of ideals
2
2
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 nontrivial 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.
1

1
13


Farzad
Shaveisi
Razi University
Razi University
Iran
f.shaveisi@ipm.ir
Arc
artinian ring
eccentricity
radius
regular digraph
The harmonic index of subdivision graphs
2
2
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.
1

15
27


Bibi Naimeh
Onagh
Golestan University
Golestan University
Iran
bn.onagh@gu.ac.ir
harmonic index
subdivision
$S$sum
inverse degree
Zagreb index
Splices, Links, and their EdgeDegree Distances
2
2
The edgedegree distance of a simple connected graph G is defined as the sum of the terms (d(eG)+d(fG))d(e,fG) over all unordered pairs {e,f} of edges of G, where d(eG) and d(e,fG) 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 edgedegree distance under two graph products called splice and link.
1

29
42


Mahdieh
Azari
Kazerun Branch, Islamic Azad University
Kazerun Branch, Islamic Azad University
Iran
mahdie.azari@gmail.com


Hojjatollah
Divanpour
Shiraz Technical College, Technical and Vocational University
Shiraz Technical College, Technical and Vocational
Iran
h.divanpour@yahoo.com
Distance
degree
edgedegree distance
splice of graphs
link of graphs
On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph
2
2
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}.
1

43
50


Hanyuan
Deng
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China
College of Mathematics and Computer Science,
China
hydeng@hunnu.edu.cn


S.
Balachandran
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
Department of Mathematics, School of Humanities
India
bala@maths.sastra.edu


S. K.
Ayyaswamy
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
Department of Mathematics, School of Humanities
China


Y. B.
Venkatakrishnan
Department of Mathematics, School of Humanities and Sciences,SASTRA University, Thanjavur, India
Department of Mathematics, School of Humanities
China
venkatakrish2@maths.sastra.edu
Average eccentricity
harmonic index
signless Laplacian eigenvalue
extremal value