For a graph G = (V, E), a subset S ⊆ V (G) is an equivalence dominating set if for every vertex v ∈ V (G) \ S, there exist two vertices u, w ∈ S such that the subgraph induced by {u, v, w} is a path. The equivalence domination number is the minimum cardinality of an equivalence dominating set of G, and the upper equivalence domination number is the maximum cardinality of a minimal equivalence dominating set of G. We explore relationships between total domination and equivalence domination. Then we determine the extremal graphs having large equivalence domination numbers.
Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-15463 |
Date | 10 September 2013 |
Creators | Arumugam, S., Chellali, Mustapha, Haynes, Teresa W. |
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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