SELF SWITCHING OF SOME LINE GRAPHS

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Published: Dec 6, 2025
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By a graph G = (V,E), we mean a finite undirected graph without loops and multiple edges. Let G be a graph and σ ⊆ V be a non–empty subset of V . G^σ is the graph obtained from G by removing all edges between σ and its complement V - σ and adding all non-edges between σ and V - σ as edges. Then σ is said to be a self switching of G if G≅ G^σ. It can also be referred to as k-vertex self switching where k = |σ|. The set of all self switchings of the graph G with cardinality k is represented by SS_k (G) and its cardinality by ss_k (G). In this paper, we find k-vertex self switching, ss_k of line graphs of path, cycle and necessary and sufficient condition for σ to be a k-vertex self switching in a line graph of complete bipartite graph

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S.S.Athithiya , C. Jayasekaran

Abstract

By a graph  we mean a finite undirected graph without loops and multiple edges. Let be a graph and  be a non–empty subset of is the graph obtained from  by removing all edges between  and its complement  and adding all non-edges between and as edges. Then is said to be a self switching of if . It can also be referred to as k-vertex self switching where  The set of all self switchings of the graph  with cardinalityis represented by  and its cardinality by . In this paper, we find -vertex self switching,  of line graphs of path, cycle and necessary and sufficient condition for  to be a -vertex self switching in a line graph of complete bipartite graph

Article Details

Issue
Vol. 38 No. 12s (2025)
Section
Articles