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Title: | A Note on Defensive Alliances in Graphs |
Authors: | Gerd H. Fricke Linda M. Lawson |
Issue Date: | 2003 |
Publisher: | Bulletin of the Institute of Combinatorics and Its Applications |
Abstract: | A defensive alliance in a graph G = (V, E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈S, the number of neighbors it has in S plus one (counting v) is at least as large as the number of neighbors it has in V - S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in V - S. We prove two conjectures posed by Hedetniemi, Hedetniemi, and Kristiansen in their introductory paper on alliances. |
URI: | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/7600 |
Appears in Collections: | Articles to be qced |
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A Note on Defensive Alliances in Graphs.pdf Restricted Access | 1.05 MB | Adobe PDF | View/Open Request a copy |
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