In this paper, we define fuzzy graph chains, which comprise vertex identification. These graphs are isomorphic graphs, provide that after applying various features to the chain of as special .

As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c (G) of such a smallest set we relate to γc(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c (T ) in terms of minimum valency and diameter. For trees the inequality γ c (T ) ≤ n− k − 1 is known to hold, we determine the class o...

Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...

A connected dominating set of a graph G = (V, E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F |) time.