Edge Pair Sum Labeling of Some Subdivision of Graphs
نویسندگان
چکیده
An injective map f : E(G) → {±1,±2, · · · ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f∗ : V (G) → Z − {0} defined by f∗(v) = ∑ e∈Ev f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f∗(V (G)) is either of the form { ±k1,±k2, · · · ,±k p 2 } or { ±k1,±k2, · · · ,±k p−1 2 } ∪ { ±k p+1 2 } according as p is even or odd. A graph which admits edge pair sum labeling is called an edge pair sum graph. In this paper, we prove that the subdivision of graph such as bistar S(Bm,n), Pn ⊙ k1, triangular snake S(Tn) if n is odd, double triangular snake D(Tn), double quadrilateral snake D(Qn), double alternative triangular snake DA(Tn) and double alternative quadrilateral snake DA(Qn) are edge pair sum graph.
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