Full domination in graphs

• Autorzy: Robert C. Brigham , Gary Chartrand , Ronald D. Dutton , Ping Zhang
• Języki publikacji: EN

Abstrakty

EN

For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_{FH}(G)$. A full dominating set of G of cardinality $γ_{FH}(G)$ is called a $γ_{FH}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.

Słowa kluczowe

EN

full domination; full star domination; full closed domination; full open domination

Kategorie tematyczne

• 05C12: Distance in graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 43-62

Daty

wydano

2001

otrzymano

2000-07-05

poprawiono

2000-10-17

Twórcy

autor

Robert C. Brigham

• Department of Mathematics, University of Central Florida, Orlando, FL 32816

autor

Gary Chartrand

• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008

autor

Ronald D. Dutton

• Program of Computer Science, University of Central Florida, Orlando, FL 32816

autor

Ping Zhang

• Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008

Bibliografia

• [1] T. Gallai, Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest, Eötvös Sect. Math. 2 (1959) 133-138.
• [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
• [4] S.R. Jayaram, Y.H.H. Kwong and H.J. Straight, Neighborhood sets in graphs, Indian J. Pure Appl. Math. 22 (1991) 259-268.
• [5] E. Sampathkumar and P.S. Neeralagi, The neighborhood number of a graph, Indian J. Pure Appl. Math. 16 (1985) 126-136.
• [6] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38 (Amer. Math. Soc. Providence, RI, 1962).

Identyfikatory

DOI

10.7151/dmgt.1132