I.C. Ross and F. Harary. The square of a tree. Bell System Tech. J., 39:641--647, 1960.  Home/Search   Document Not in Database   Summary   Related Articles

....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 that the mathematical ....

....[14] ffl A Hamiltonian cycle in G k , k 3, can be found in linear time given G. When G is a tree, the existence of a Hamiltonian cycle in G 2 can be determined in linear time. We conclude with open problems. 2 Tree Square Roots Tree square roots were first considered by Ross and Harary [23], who showed that they are unique up to isomorphism. Figure 1 presents a tree and its square. In this section, T 2 T Figure 1: A tree and its square. we present an O(jV j jEj) algorithm for finding the tree square root of a given graph G = V; E) We will show that the leaves of the tree ....

I.C. Ross and F. Harary. The square of a tree. Bell System Tech. J., 39:641--647, 1960.

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