مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Journal Paper

Title

Some algebraic properties of the subdivision graph of a graph

Pages

  297-307

Abstract

 Let $G=(V,E)$ be a connected graph with the vertex-set $V$ and  the edge-set $E$.    The subdivision graph $S(G)$ of the graph $G$ is obtained from $G$ by adding a vertex in the middle of every edge of $G$.  In this paper, we investigate some properties of the graphs  $S(G)$ and $L(S(G))$, where $L(S(G))$ is the Line graph of $S(G)$. We will see that $S(G)$ and  $L(S(G))$  inherit some  properties of $G$.    For instance, we show that if $G \ncong C_n$, then $Aut(G) \cong Aut(L(S(G)))$ (as abstract groups), where $C_n$ is the cycle of order $n$.

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