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Edge pair sum labeling of some cartesian product of graphs

P. Jeyanthi

Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, India

E-mail Address: jeyajeyanthi@rediffmail.com

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and

T. Saratha Devi

Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti 658502, India

E-mail Address: rajanvino03@gmail.com

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https://doi.org/10.1142/S1793830916500245Cited by:2 (Source: Crossref)

Abstract

Let $G$ $G$ be a $(p, q)$ $(p, q)$ graph. An injective map $f : E (G) \to {\pm 1, \pm 2, \dots, \pm q}$ $f : E (G) \to {\pm 1, \pm 2, \dots, \pm q}$ is said to be an edge pair sum labeling if the induced vertex function $f^{*} : V (G) \to Z - {0}$ $f^{*} : V (G) \to Z - {0}$ defined by $f^{*} (v) = \sum_{e ϵ E_{v}} f (e)$ $f^{*} (v) = \sum_{e ϵ E_{v}} f (e)$ is one-to-one where $E_{v}$ $E_{v}$ denotes the set of edges in $G$ $G$ that are incident with the vertex $v$ $v$ and $f^{*} (V (G))$ $f^{*} (V (G))$ is either of the form ${\pm k_{1}, \pm k_{2}, \dots, \pm k_{\frac{p}{2}}}$ ${\pm k_{1}, \pm k_{2}, \dots, \pm k_{\frac{p}{2}}}$ or ${\pm k_{1}, \pm k_{2}, \dots, \pm k_{\frac{p - 1}{2}}} \cup {\pm k_{\frac{p + 1}{2}}}$ ${\pm k_{1}, \pm k_{2}, \dots, \pm k_{\frac{p - 1}{2}}} \cup {\pm k_{\frac{p + 1}{2}}}$ accordingly as $p$ $p$ is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper, we prove that the graphs $(P_{2} \times P_{m}) ⊙ K_{n}^{c}$ $(P_{2} \times P_{m}) ⊙ K_{n}^{c}$ , $(P_{m} \times C_{3})$ $(P_{m} \times C_{3})$ , book graph and $N Q (m)$ $N Q (m)$ admit edge pair sum labeling.

Keywords:

AMSC: 05C78

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