INDUCED $V_4-$ MAGIC LABELING OF SOME STAR AND PATH RELATED GRAPHS

Abstract

Let $V_4=\{ 0,a,b,c \}$ be the Klein-4-group with identity element $0$ and $G = (V (G),E(G)),$ be the graph with vertex set $V(G)$ and edge set $E(G).$ Let $f: V(G) \rightarrow V_4 $ be a vertex labeling and $f^{*}: E(G)\rightarrow V_4$ denote the induced edge labeling of $f$ defined by $f^* (uv)=f (u)+f(v)$ for all $uv\in E(G).$ Then $f^*$ again induces a vertex labeling $f^{**}: V(G)\rightarrow V_4$ defined by $f^{**}(u)=\Sigma f^*(uv)$ where the summation is taken over all the vertices $v$ which are adjacent to $u.$ A graph $G=(V(G),E(G))$ is said to be an induced $V_4$-Magic graph if there exists a non zero vertex labeling $f: V(G) \rightarrow V_4 $ such that $f\equiv f^{**}.$ The function $f,$ so obtained is called an induced $V_4$-Magic labeling of $G.$ In this paper we discuss Induced $V_4$ magic labeling of some graphs and the Induced $V_4$ magic labeling of some star and path related graphs.