Total domination changing and stable graphs upon vertex removal |
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Authors: | Wyatt J Desormeaux Teresa W Haynes |
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Institution: | a Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002, USAb Department of Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa |
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Abstract: | A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs. |
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Keywords: | Total domination Vertex removal stable Vertex removal changing |
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