SWITCHING OF VERTEX ON SOME GRAPHS WITH GEOMETRIC MEAN 3-EQUITABLE LABELING

SWITCHING OF VERTEX ON SOME GRAPHS WITH GEOMETRIC MEAN 3-EQUITABLE LABELING

R. K. Dharsanda, P. I. Andharia, P. P. Andharia

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Abstract

For a graph H with a vertex set P(H) and an edge set Q(H), if map g : P(H) ! f0; 1; 2g and its induced map g  : Q(H) ! f0; 1; 2g de ned by g (xy) = d p g(x)g(y)e; 8xy 2 Q(H), satis es the absolute di erence of the number of vertices (edges) with labeled x and labeled y is at most 1( where 8x; y 2 f0; 1; 2g) then g is called a geometric mean 3 - equitable labeling. In this paper, we investigate a geometric mean 3-equitable labeling of the graph obtained from switching of any vertex with degree one in path Pr for r   1 ( mod 3 ), switching of any vertex other than the support vertices in path Pr for r   1; 2 ( mod 3 ) and switching of any vertex in cycle Cr for r   1; 2 ( mod 3 ).

Keywords

Switching operation, jewel graph, mean graph, path, cycle.