Some recent results on domination in graphs | Zendy

Michael D. Plummer | Zendy

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Some recent results on domination in graphs

Author(s) -

Michael D. Plummer

Publication year - 2006

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.1338

Subject(s) - mathematics , combinatorics , domination analysis , graph , vertex (graph theory)

In this paper, we survey some new results in four areas of domination in graphs, namely: (1) the toughness and matching structure of graphs having domination number 3 and which are “critical” in the sense that if one adds any missing edge, the domination number falls to 2; (2) the matching structure of graphs having domination number 3 and which are “critical” in the sense that if one deletes any vertex, the domination number falls to 2; (3) upper bounds on the domination number of cubic graphs; and (4) upper bounds on the domination number of graphs embedded in surfaces.

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