Title

On graphs having equal domination and codomination numbers

Abstract

In a graph G = (V, E), a set S ⊂ V is a dominating set if each vertex of V-S is adjacent to at least one vertex in S. The domination number γ(G) is the smallest order of a dominating set of G and the codomination number of G, written γ(Ḡ), is the domination number of its complement. We investigate conditions under which graphs have equal domination and codomination numbers. In particular, we characterize graphs for which γ(G) = γ(Ḡ) = 2 and establish properties of graphs for which γ(G) = γ(Ḡ) ≥ 3. Finally, we construct a family of graphs having γ(G) = γ(Ḡ).

Publication Date

12-1-1996

Publication Title

Utilitas Mathematica

Volume

50

Number of Pages

53-64

Document Type

Article

Personal Identifier

scopus

Socpus ID

0030300314 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0030300314

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