engleski

K-domination sets on double linear hexagonal chains

A hexagonal chain is a catacondensed hexagonal system in which every hexagon is adjacent to at most two hexagons. Double linear hexagonal chain is consisted of 2 condensed linear hexagonal chains. For any graph G by V(G) and E(G) we denote the vertex-set and the edge-set of G, respectively. For graph G subset D of the vertex-set of G is called k-dominating set, k\geq 1, if for every vertex v in V(G)\D, there exists at least one vertex w in D, such that d(v, w) less or equal to k. The k-domination number gamma_k(G) is the cardinality of the smallest k-dominating set. The 1-domination set (number) is also called domination set (number). In this paper I determine minimal k-dominating sets for double linear hexagonal chain B(2h) of length h and give exact results for its k-dominaton number.

k-dominating set; k-domination number; double linear hexagonal chain.

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