#### Document Type

Journal Article

#### Department/Unit

Department of Mathematics

#### Title

Edge-magic indices of (n, n – 1)-graphs

#### 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 → Zp is a constant mapping, where f+ (u) ≡ ∑ uv ∈ E f(uv) (mod p). A necessary condition of edge-magicness is p {divides} q(q+1). The edge magic index of a graph G is the least positive integer k such that the k-fold of G is edge-magic. In this paper, we prove that for any multigraph G with n vertices, n - 1 edges having no loops and no isolated vertices, the k-fold of G is edge-magic if n and k satisfy a necessary condition for edge-magicness and n is odd. For n even we also have some results on full m-ary trees and spider graphs. Some counterexamples of the edge-magic indices of trees conjecture are given. © 2002.

#### Keywords

Edge-magic, edge-magic index, spider graph, tree

#### Publication Date

2002

#### Source Publication Title

Electronic Notes in Discrete Mathematics

#### Volume

11

#### Start Page

443

#### End Page

458

#### Publisher

Elsevier

#### DOI

10.1016/S1571-0653(04)00089-7

#### Link to Publisher's Edition

http://dx.doi.org/10.1016/S1571-0653(04)00089-7

#### ISSN (print)

15710653

#### Recommended Citation

Shiu, Wai Chee,
C.B.Lam Peter,
and
Sin-Min Lee.
"Edge-magic indices of (n, n – 1)-graphs."
*Electronic Notes in Discrete Mathematics*
11
(2002): 443-458.