Odd-Even Sum Labeling of some Graphs

Abstract

A $(p,q)$ graph $G=(V,E)$ is said to be an odd-even sum graph if there exists an injective function $f:V(G)\rightarrow\lbrace\pm 1,\pm 3 \pm 5, ...,\pm (2p-1)\rbrace$ such that the induced mapping $f^{*}:E(G)\rightarrow\lbrace 2,4,6, ...,2q\rbrace$ defined by $f^{*}(uv)=f(u)+f(v)~\forall~uv\in E(G)$ is bijective. The function $f$ is called an odd-even sum labeling of $G$. In this paper we study odd-even sum labeling of path $P_{n}(n\geq2)$, star $K_{1,n}(n\geq 1)$, bistar $B_{m,n}$,$S(K_{1,n})$, $B(m,n,k)$ and some standard graphs.