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THE FORCING TOTAL EDGE DOMINATION NUMBER OF A GRAPH

  J.Deva Raj1, V. Sujin Flower2
Journal Title :

Asian Journal of Applied Research
DOI :
Page No :

1-7
Volume :

1
Issue :

4
Month/Year :

4/2015

Article (PDF)

Keywords

total edge domination number, forcing edge domination number, forcing total edge domination number.

Abstract

Let G be a connected graph and S a minimum total edge dominating set of G. A subsetT⊆Sis called aforcing subset for S if S is the unique minimum total edge dominating set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. Theforcing total edge domination number of S, denoted by〖f_γ〗_te (S), is the cardinality of a minimum forcing subset of S. The forcing total edge domination number of G, denoted by〖f_γ〗_te (G), is〖f_γ〗_te (G)=min{〖f_γ〗_te (S)}, where the minimum is taken over all minimum total edge dominating sets S in G. Some general properties satisfied by this concept are studied. Connected graphs with forcing total edge domination number 0 or 1 are characterized. Some realization results are given.