Odd-even sum labeling of some graphs

A $(p,q)$ graph $G=(V,E)$ is said to be an odd-even sum graph if there exists an injective function $f:V(G)rightarrowlbracepm 1,pm 3 pm 5, ...,pm (2p-1)rbrace$ such that the induced mapping $f^{*}:E(G)rightarrowlbrace 2,4,6, ...,2qrbrace$ defined by $f^{*}(uv)=f(u)+f(v)~forall~uvin E(G)$ 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 $P_{n}(ngeq2)$, star $K_{1,n}(ngeq 1)$, bistar $B_{m,n}$,$S(K_{1,n})$, $B(m,n,k)$ and some standard graphs.