@Article{Shaveisi2017,
author="Shaveisi, Farzad",
title="The central vertices and radius of the regular graph of ideals",
journal="Transactions on Combinatorics",
year="2017",
volume="6",
number="4",
pages="1-13",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2017.21472",
url="http://toc.ui.ac.ir/article_21472.html"
}
@Article{Onagh2017,
author="Onagh, Bibi Naimeh",
title="The harmonic index of subdivision graphs",
journal="Transactions on Combinatorics",
year="2017",
volume="6",
number="4",
pages="15-27",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2017.21471",
url="http://toc.ui.ac.ir/article_21471.html"
}
@Article{Azari2017,
author="Azari, Mahdieh
and Divanpour, Hojjatollah",
title="Splices, Links, and their Edge-Degree Distances",
journal="Transactions on Combinatorics",
year="2017",
volume="6",
number="4",
pages="29-42",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2017.21614",
url="http://toc.ui.ac.ir/article_21614.html"
}
@Article{Deng2017,
author="Deng, Hanyuan
and Balachandran, S.
and Ayyaswamy, S. K.
and Venkatakrishnan, Y. B.",
title="On the average eccentricity, the harmonic index and the largest signless Laplacian eigenvalue of a graph",
journal="Transactions on Combinatorics",
year="2017",
volume="6",
number="4",
pages="43-50",
abstract="The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity $ecc\left(G\right)$ of a graph $G$ is the mean value of eccentricities of all vertices of $G$. The harmonic index $H\left(G\right)$ 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 $n\geq 2\Delta$. 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}.",
issn="2251-8657",
doi="10.22108/toc.2017.21470",
url="http://toc.ui.ac.ir/article_21470.html"
}
@Article{Zhu2017,
author="Zhu, Xiaomin
and Feng, Lihua
and Liu, Minmin
and Liu, Weijun
and Hu, Yuqin",
title="Some topological indices and graph properties",
journal="Transactions on Combinatorics",
year="2017",
volume="6",
number="4",
pages="51-65",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2017.21467",
url="http://toc.ui.ac.ir/article_21467.html"
}