Zero forcing in Benzenoid network
DOI:
https://doi.org/10.22199/issn.071762792019050064Keywords:
Zero forcing set, Pyrene networks, Circumpyrene networks, Circumtrizene networksAbstract
A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)\S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a power dominating set of G. A dynamic coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all remaining vertices being noncolored. At each discrete time interval, a colored vertex with exactly one noncolored neighbor forces this noncolored neighbor to be colored. The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. The zero forcing number of G, denoted Z(G), is the minimum cardinality of a zero forcing set of G. In this paper, we obtain the zero forcing number for certain benzenoid networks.
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