Zero forcing in Benzenoid network


  • J. Anitha Easwari Engineering College.
  • Indra Rajasingh Vellore Institute of Technology.



Zero forcing set, Pyrene networks, Circum-pyrene networks, Circum-trizene networks


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 non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored 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.


Author Biographies

J. Anitha, Easwari Engineering College.

Department of Mathematics.

Indra Rajasingh, Vellore Institute of Technology.

School of Advanced Sciences.


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How to Cite

J. . Anitha and I. Rajasingh, “Zero forcing in Benzenoid network”, Proyecciones (Antofagasta, On line), vol. 38, no. 5, pp. 999-1010, Dec. 2019.