Title of article :
Total domination and matching numbers in graphs with all vertices in triangles
Author/Authors :
Henning، نويسنده , , Michael A. and Yeo، نويسنده , , Anders، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Abstract :
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. The matching number of G is the maximum cardinality of a matching of G . A set S of vertices in 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 . We prove that if all vertices of G belong to a triangle, then the total domination number of G is bounded above by its matching number. We in fact prove a slightly stronger result and as a consequence of this stronger result, we prove a Graffiti conjecture that relates the total domination and matching numbers in a graph.
Keywords :
matching number , Total domination number
Journal title :
Discrete Mathematics
Journal title :
Discrete Mathematics