The Cycle Neighbor Polynomial of a graph G is defined as, CN * [G, z] = Σ c(G) k=0 c k (G)z k , where c 0 (G) is the number of isolated vertices, c 1 (G) is the number of non isolated vertices which does not belong to any cycle of G, c 2 (G) is the number of bridges and c k (G) is the number of cycles of length k in G for g(G) ≤ k ≤ c(G) with g(G) and c(G) are respectively the girth and circumference of G. This paper deals with the cycle neighbor polynomial of some graph operations, graph modifications and that of graphs derived from the given graph.
is called a dominating set if every vertex in G is either in D or is adjacent to an element of D . A simple graph G is said to be 0 T , if for any two distinct vertices u and v of , G either one of u and v is isolated or there exists an edge e such that either e is incident with u but not with v or e is incident with v but not with u . If D of a dominating set D of the graph G is a 0 T graph, then it is called a 0
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