Zero Forcing in Snake Graph
J. Anitha

J. Anitha, Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, Chennai (Tamil Nadu), India
Manuscript received on 05 February 2019 | Revised Manuscript received on 18 February 2019 | Manuscript Published on 04 March 2019 | PP: 133-136 | Volume-7 Issue-5S2 January 2019 | Retrieval Number: ES2019017519/19©BEIESP
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Abstract: 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, obtain the zero forcing number for hexagonal chain torus, alternate quadrilateral snake and double quadrilateral snake. AMS Subject Classification— 05C69, 05C85, 05C90 and 05C20.
Keywords: Zero Forcing Set, Hexagonal Chain Torus, Alternate Quadrilateral Snake, Double Quadrilateral Snake.
Scope of the Article: Cryptography and Applied Mathematics