Switching of vertex on some graphs with geometric mean 3-equitable labeling

Abstract

For a graph H with a vertex set P(H) and an edge set Q(H), if map g : P(H) → {0, 1, 2} and its induced map g*: Q(H) → {0, 1, 2} defined by g* (xy) =Γ√g(x)g(y)ꓶ; ∀xy ∈ Q(H), satisfies the absolute difference of the number of vertices (edges) with labeled x and labeled y is at most 1( where ∀x, y ∈ {0, 1, 2}) 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 ).