Trees with equal total and total restrained domination numbers | Zendy

Hongyu Chen | Zendy; Xue-gang Chen | Zendy; Wai Chee Shiu | Zendy

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Trees with equal total and total restrained domination numbers

Author(s) -

Hongyu Chen,

Xue-gang Chen,

Wai Chee Shiu

Publication year - 2008

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1391

Subject(s) - dominating set , domination analysis , mathematics , combinatorics , graph , cardinality (data modeling) , set (abstract data type) , discrete mathematics , vertex (graph theory) , computer science , data mining , programming language

For a graph G = (V; E), a set S V (G) is a total dominating set if it is dominating and both hSi has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S V (G) is a total restrained dominating set if it is total dominating and hV (G) Si has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.

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