F. Escalante, L. Montejano, and T. Rojano. Characterization of n-path graphs and of graphs having nth root. J. Combin. Theory B, 16:282--289, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Initiation Award CCR9109289. E mail: skiena sbcs.sunysb.edu 1. S 1in G i = G, 2. v i 2 G i , 3. v i 2 G j if and only if v j 2 G i . Characterizations of squares of digraphs were given by Geller [13] and of n th power of graphs and digraphs was given by Escalante, Montejano, and Rojano [7]. Ross and Harary [23] showed that a graph has an unique tree square root (up to isomorphism) if it has a tree as its square root. Although many properties of the square roots of graphs have been discovered, no efficient algorithms for finding the square root of a graph was known. One reason is ....

F. Escalante, L. Montejano, and T. Rojano. Characterization of n-path graphs and of graphs having nth root. J. Combin. Theory B, 16:282--289, 1974.

....i 2 H i . ffl v i 2 H j if and only if v j 2 H i . ffl [ i H i = H . This is not a polynomial characterization in that it does not lead to a polynomial time algorithm for recognizing square graphs. Similar characterizations were provided for the squares of directed graphs [4] and the k th powers [1]. Several results have been obtained on the powers of special classes of graphs, or in the case where the power of a graph belongs to a special class. Ross Harary [10] showed that the tree square roots of a graph, when they exist, are unique up to isomorphisms. Harary, Karp Tutte [5] provided ....

F. Escalante, L. Montejano and T. Rojano, Characterization of n-path graphs and of graphs having n'th root, Journal of Combinatorial Theory (Series B), 16 (1974), pp. 282--289.

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