Modified ?-graph G(?m) of some special graphs

By : R. Kala, V. Anusuya

Page No: 131-143

Abstract
Gerd H. Frickle et al. [1] introduced ? -graph of a graph. Consider the family of all ? - sets in a graph G and we define G(? ) = (V (? ), E(? )) to be the graph whose vertices correspond 1 to 1 with the ? -sets of G and two ? -sets say S1 and S2 are adjacent in G(? ) if there exist a vertex v ? S1 and a vertex w ? S2 such that v is adjacent to w and S1 = S2 – {w} ? {v} or equivalently S2 = S1 – {v} ? {w}. The concept of ? -graph inspired us to define Modified ? -graph of a graph. Consider the family of all ? -sets of a graph G and define the modified ? -graph G(? m) = (V (? m), E(? m)) of G to be the graph whose vertices V (? m) correspond 1-1 with the ? -sets of G and two ? -sets S1 and S2 form an edge in G(? m) if there exists a vertex v ? S1 and w ? S2 such that S1 = S2 – {w} ? {v} and S1 = S2 – {v} ? {w}. In this paper we determine G(? m) of some special graphs.

Authors :
V. Anusuya : Department of Mathematics, S.T.Hindu College, Nagercoil- 629 002, Tamil Nadu, India
R. Kala : Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 629 012, Tamil Nadu, India.