2018-09-21T22:45:38Z
http://toc.ui.ac.ir/?_action=export&rf=summon&issue=3943
Transactions on Combinatorics
Trans. Comb.
2251-8657
2251-8657
2017
6
4
The central vertices and radius of the regular graph of ideals
Farzad
Shaveisi
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
2017
12
01
1
13
http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf
Transactions on Combinatorics
Trans. Comb.
2251-8657
2251-8657
2017
6
4
The harmonic index of subdivision graphs
Bibi Naimeh
Onagh
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
2017
12
01
15
27
http://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf
Transactions on Combinatorics
Trans. Comb.
2251-8657
2251-8657
2017
6
4
Splices, Links, and their Edge-Degree Distances
Mahdieh
Azari
Hojjatollah
Divanpour
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
2017
12
01
29
42
http://toc.ui.ac.ir/article_21614_033f4714ff9a47c358a450a46e9a3122.pdf
Transactions on Combinatorics
Trans. Comb.
2251-8657
2251-8657
2017
6
4
On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph
Hanyuan
Deng
S.
Balachandran
S. K.
Ayyaswamy
Y. B.
Venkatakrishnan
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
2017
12
01
43
50
http://toc.ui.ac.ir/article_21470_6107bccf810358fdefb9471c7d0ba0a8.pdf
Transactions on Combinatorics
Trans. Comb.
2251-8657
2251-8657
2017
6
4
Some topological indices and graph properties
Xiaomin
Zhu
Lihua
Feng
Minmin
Liu
Weijun
Liu
Yuqin
Hu
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
2017
12
01
51
65
http://toc.ui.ac.ir/article_21467_d05e2410fc3d5c5560f3430866b8af0e.pdf