#### Document Type

Journal Article

#### Department/Unit

Department of Mathematics

#### 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.

#### Publication Year

2015

#### Journal Title

Utilitas Mathematica

#### Volume number

97

#### Publisher

Utilitas Mathematica Publishing Incorporated

#### First Page (page number)

271

#### Last Page (page number)

286

#### Referreed

1

#### ISSN (print)

03153681

#### Keywords

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

#### Citation

Shiu, Wai Chee,
Peter Che Bor Lam,
and
Sin-Min Lee.
"Edge-magic index sets of square of paths."
*Utilitas Mathematica*
97
(2015): 271-286.