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Volume 20 No 22 (2022)
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SOME NEW FAMILIES OF EDGE PAIR MEAN GRAPHS
M. Krishna Kumar and T. Saratha Devi
Abstract
Let G be a (p,q) graph. An injective map f:E(G)⟶{±1,±2,±3,⋯,±q} is said to be an edge pair mean labeling if the induced vertex function f^*:V(G)⟶Z-{0} defined by f^* (v)=⌈(∑_(e∈E_v)▒ f(e))/(|E_v |)⌉ is one-one, where E_v denotes the set of edges in G that are incident with a vertex v and f^* (V(G)) is either of the form {±k_1,±k_2,±k_3,⋯,±k_(p/2)} or {±k_1,±k_2,±k_3,⋯,±k_((p-1)/2)}∪{k_((p+1)/2)} according as p is even or odd. A graph with an edge pair mean labeling is called an edge pair mean graph.. In this paper, we prove that the graphs P_n∪P_n, C_n∪C_n, K_(1,n)∪K_(1,n) admit edge pair mean labeling.
Keywords
Throughout this paper we have considered only simple and undirected graph.
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