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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

ISSN (print)

15710653

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