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An algebraic approach is proposed which can be used to solve different problems on fasci-agraphs and rotagraphs. A particular instance of this method computes the domination number of fasciagraphs and rotagraphs in O(logn) time, where n is the number of monographs of such a graph. Fasciagraphs and rotagraphs include complete grid graphs Pk 0 P, and graphs… (More)

Roman domination is an historically inspired variety of domination in graphs, in which vertices are assigned a value from the set {0, 1, 2} in such a way that every vertex assigned the value 0 is adjacent to a vertex assigned the value 2. The Roman domination number is the minimum possible sum of all values in such an assignment. Using an algebraic approach… (More)

Mixed connectivity is a generalization of vertex and edge connectivity. A graph is (p, 0)-connected, p > 0, if the graph remains connected after removal of any p − 1 vertices. A graph is (p, q)-connected, p ≥ 0, q > 0, if it remains connected after removal of any p vertices and any q − 1 edges. Cartesian graph bundles are graphs that generalize both… (More)