Connected domination in maximal outerplanar graphs

Abstract

A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V∖S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). We show that the connected domination number of a maximal outerplanar graph G is bounded by min{⌊n+k2⌋−2,⌊2(n−k)3⌋}, where k is the number of vertices of degree 2 in G. Moreover, we improve this upper bound for striped maximal outerplanar graphs and characterize the graphs that achieve the bound.