IJPAM: Volume 116, No. 2 (2017)

Title

SOME RESULTS ON DUPLICATION SELF VERTEX SWITCHINGS

Authors

C. Jayasekaran$^1$, V. Prabavathy$^2$
$^1$Department of Mathematics
Pioneer Kumaraswamy College
Nagercoil, 629 003, INDIA
$^2$Department of Mathematics
Vivekananda College
Agasteeswaram, 629 701, INDIA

Abstract

A vertex $v \in V(G)$ is said to be a $self ~vertex ~switching$ of $G$ if $G$ is isomorphic to $G^{v}$, where $G^{v}$ is the graph obtained from $G$ by deleting all edges of $G$ incident to $v$ and adding all edges incident to $v$ which are not in $G$. Duplication of a vertex $v$ of graph $G$ produces a new graph $G^{'}$ by adding a new vertex $v^{'}$ such that $N(v^{'}) = N(v)$. In other words a vertex $v{'}$ is said to be duplication of $v$ if all the vertices which are adjacent to $v$ in $G$ are also adjacent to $v^{'}$ in $G^{'}$. A vertex $v$ is called a $duplication ~self ~vertex ~ switching$ of a graph $G$ if the resultant graph obtained after duplication of $v$ has $v$ as a self vertex switching. In this paper, we give some properties of duplication self vertex switching.

History

Received: 2017-05-02
Revised: 2017-09-27
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C60
Key Words and Phrases: switching, self vertex switching, duplication self vertex switching, $dss_{1}(G)$

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How to Cite?

DOI: 10.12732/ijpam.v116i2.14 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 427 - 435


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