Efficient domination in knights graphs

Authors

Anne Sinko, College of Saint Benedict/Saint John's UniversityFollow
Peter J. Slater

Document Type

Article

Publication Date

12-2006

Disciplines

Discrete Mathematics and Combinatorics | Mathematics

Abstract

The influence of a vertex set S ⊆V(G) is I(S) = Σ_v∈S(1 + deg(v)) = Σ_v∈S |N[v]|, which is the total amount of domination done by the vertices in S. The efficient domination number F(G) of a graph G is equal to the maximum influence of a packing, that is, F(G) is the maximum number of vertices one can dominate under the restriction that no vertex gets dominated more than once.

In this paper, we consider the efficient domination number of some finite and infinite knights chessboard graphs.

Recommended Citation

Sinko A, Slater PJ. 2006. Efficient domination in knights graphs. AKCE International Journal of Graphs and Combinatorics 3(2): 193-204.