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- W2044231347 abstract "The Path Length Distribution (PLD) of a ( p, q ) graph is defined to be the array ( X 0 , X 1 , X 2 , …, X p -1 ), where X 0 is the number of (unordered) pairs of vertices which have no path connecting them and X l , 1 ≦ l ≦ p -1, is the number of pairs of vertices which are connected by a path of length l (see [1, 2]). The topic of this paper is the occurence of non-isomorphic graphs having the same path length distribution. For trees, a constructive procedure is given, showing that for any positive integer N there exist N non-isomorphic trees of diameter four which have the same PLD. Also considered are PLD- maximal graphs — those graphs with p vertices such that all pairs of vertices are connected by a path of length l for 2 ≦ l ≦ p -1. In addition to providing more examples of non-isomorphic graphs having the same PLD, PLD-maximal graphs are of intrinsic interest. For PLD-maximal graphs, we give sufficient degree and edge conditions and a necessary edge condition." @default.
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- W2044231347 date "1973-09-01" @default.
- W2044231347 modified "2023-09-26" @default.
- W2044231347 title "Theory of path length distributions I" @default.
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- W2044231347 doi "https://doi.org/10.1016/0012-365x(73)90035-6" @default.
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