Odd-even sum labeling of some graphs

K Monika, K Murugan


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, odd-even sum labeling of path $P_{n}(n\geq2)$,Star $K_{1,n}(n\geq 1)$,Bistar $B_{m,n}$,$spl(K_{1,n})$,$B(m,n,k)$ and some other graphs are studied.

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