Strongly distance-balanced graphs and graph products1
نویسندگان
چکیده
A graph G is strongly distance-balanced if for every edge uv of G and every i ≥ 0 the number of vertices x with d(x, u) = d(x, v)−1 = i equals the number of vertices y with d(y, v) = d(y, u) − 1 = i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distancebalanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distance-balanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distancebalanced graphs and an algorithm of time complexity O(mn) for their recognition, where m is the number of edges and n the number of vertices of the graph in question, are given.
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