#### Document Type

Journal Article

#### Department/Unit

Department of Mathematics

#### Language

English

#### 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.

#### Keywords

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

#### Publication Date

2015

#### Source Publication Title

Utilitas Mathematica

#### Volume

97

#### Start Page

271

#### End Page

286

#### Publisher

Utilitas Mathematica Publishing Incorporated

#### Peer Reviewed

1

#### ISSN (print)

03153681

#### APA Citation

Shiu, W.,
Lam, P.,
&
Lee, S.
(2015).
Edge-magic index sets of square of paths.
*
Utilitas Mathematica,
97
*
().
Retrieved from https://repository.hkbu.edu.hk/math_ja/38