Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

Let G be a simple graph. The independent domination number i(G) is the minimum cardinality among all maximal independent sets of G. Haviland (1995) conjectured that any connected regular graph G of order n and degree δn/2 satisfies i(G) ⩽ ⌈2n/3δδ/2. In this paper, we will settle the conjecture of Haviland in the negative by constructing counterexamples. Therefore a larger upper bound is expected. We will also show that a connected cubic graph G of order n ⩾ 8 satisfies i(G) ⩽ 2n/5, providing a new upper bound for cubic graphs.

Publication Year

1999

Journal Title

Discrete Mathematics

Volume number

202

Issue number

1-3

Publisher

Elsevier

First Page (page number)

135

Last Page (page number)

144

Referreed

1

DOI

10.1016/S0012-365X(98)00350-1

ISSN (print)

1872681X

Keywords

Independent domination number, Regular graph

Included in

Mathematics Commons

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