Edge-magic Index Sets of Square of Paths

Wai Chee Shiu; Peter, Che Bor Lam; Sin-Min Lee

Edge-magic Index Sets of Square of Paths

Wai Chee Shiu, Peter, Che Bor Lam, Sin-Min Lee

Department of Mathematics

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Abstract

A graph G = (V, E) with p vertices and q edges is called edge-magic if there is a bijection f : E → {1, 2, . . . , q} such that the induced mapping f+ : V → ℤ_p is a constant mapping, where f+ (u) ≡ ^∑_{v∈N (u)} f(uv) (mod p). The edge-magic index set of a graph G is the set of positive integer k such that the k-fold of G is edge-magic. In this paper, we find the edge-magic index set of the second power of a path.

Original language	English
Pages (from-to)	271-286
Number of pages	16
Journal	Utilitas Mathematica
Volume	97
Publication status	Published - Jul 2015

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Edge-magic
edge-magic index
edge-magic index set
power of path

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AB - A graph G = (V, E) with p vertices and q edges is called edge-magic if there is a bijection f : E → {1, 2, . . . , q} such that the induced mapping f+ : V → ℤp is a constant mapping, where f+ (u) ≡ ∑v∈N (u) f(uv) (mod p). The edge-magic index set of a graph G is the set of positive integer k such that the k-fold of G is edge-magic. In this paper, we find the edge-magic index set of the second power of a path.

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Edge-magic Index Sets of Square of Paths

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