Comment on “Kirchhoff index in line, subdivision and total graphs of a regular graph”
نویسندگان
چکیده
منابع مشابه
Zagreb Indices and Coindices of Total Graph, Semi-Total Point Graph and Semi-Total Line Graph of Subdivision Graphs
Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.
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Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
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A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...
متن کاملThe Laplacian Polynomial and Kirchhoff Index of the k-th Semi Total Point Graphs
The k-th semi total point graph of a graph G, , is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of edge considered. In this paper, a formula for Laplacian polynomial of in terms of characteristic and Laplacian polynomials of G is computed, where is a connected regular graph.The Kirchhoff index of is also computed.
متن کاملnote on degree kirchhoff index of graphs
the degree kirchhoff index of a connected graph $g$ is defined as the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices, where $d_i$ is the degree of the $i$-th vertex, and $r_{ij}$ the resistance distance between the $i$-th and $j$-th vertex of $g$. bounds for the degree kirchhoff index of the line and para-line graphs are determined. the special case of regular grap...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.06.015