k-vertex Anti-duplication Self Switching of Graphs
Keywords:
k-vertex self switching, anti-duplication, k-vertex anti-duplication switching, k-vertex anti-duplication self switching, AD(σG)Abstract
For a finite undirected graph and a non-empty set , the switching of by is defined as the graph which is obtained from by removing all edges between and its complement and adding as edges all non-edges between and . If , then is called as self switching of and if , then it is called as -vertex self switching. The set of all -vertex self switchings of is denoted by and its cardinality by . -vertex anti-duplication of the vertices produces a new graph by adding new vertices such that for . This paper explores the characteristics of -vertex anti-duplication, propose the concept of -vertex anti-duplication self switching and analyzes its associated properties.
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