Let G be a graph and Ḡ be the complement of G. The complementary prism GḠ of G is the graph formed from the disjoint union of G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. For example, if G is a 5-cycle, then GḠ is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, max {γ(G), γ(Ḡ)} ≤ γ (Ḡ)and max {γt(G), γt(Ḡ)} ≤ γt (Gγ), where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.
Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-18551 |
Date | 01 July 2009 |
Creators | Haynes, Teresa W., Henning, Michael A., Van Der Merwe, Lucas C. |
Publisher | Digital Commons @ East Tennessee State University |
Source Sets | East Tennessee State University |
Detected Language | English |
Type | text |
Source | ETSU Faculty Works |
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