Graphical sequences of some family of induced subgraphs

Year 2015, Volume: 2 Issue: 2, 95 - 109, 30.04.2015

S. Pirzada Bilal A. Chat Farooq A. Dar

https://doi.org/10.13069/jacodesmath.39202

Cited By: 1

Abstract

The subdivision graph $S(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. The $S_{vertex}$ or $S_{ver}$ join of the graph $G_{1}$ with the graph $G_{2}$, denoted by $G_{1}\dot{\vee}G_{2}$, is obtained from $S(G_{1})$ and $G_{2}$ by joining all vertices of $G_{1}$ with all vertices of $G_{2}$. The $S_{edge}$ or $S_{ed}$ join of $G_{1}$ and $G_{2}$, denoted by $G_{1}\bar{\vee}G_{2}$, is obtained from $S(G_{1})$ and $G_{2}$ by joining all vertices of $S(G_{1})$ corresponding to the edges of $G_{1}$ with all vertices of $G_{2}$. In this paper, we obtain graphical sequences of the family of induced subgraphs of $S_{J} = G_{1}\vee G_{2}$, $S_{ver} = G_{1}\dot{\vee}G_{2}$  and $S_{ed} = G_{1}\bar{\vee}G_{2}$. Also we prove that the graphic sequence of $S_{ed}$ is potentially $K_{4}-e$-graphical.

Keywords

Graphical sequences, Subdivision graph, Join of graphs, Split graph

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