Restrained domination in unicyclic graphs | Zendy

Johannes H. Hattingh | Zendy; Ernst J. Joubert | Zendy; Marc Loizeaux | Zendy; Andrew Plummer | Zendy; Lucas C. van der Merwe | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Restrained domination in unicyclic graphs

Author(s) -

Johannes H. Hattingh,

Ernst J. Joubert,

Marc Loizeaux,

Andrew Plummer,

Lucas C. van der Merwe

Publication year - 2009

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.1433

Subject(s) - combinatorics , mathematics , dominating set , vertex (graph theory) , graph , domination analysis , discrete mathematics , bound graph , connectivity , graph power , line graph

Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then γr(U) ≥ dn3 e, and provide a characterization of graphs achieving this bound.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research