Publications of (and about) Paul Erdös
Autor: Alavi, Yousef; Boals, Alfred J.; Chartrand, Gary; Oellermann, Ortrud R.; Erdös, Paul
Title: K-path irregular graphs. (In English)
Source: Combinatorics, graph theory, and computing, Proc. 19th Southeast. Conf., Boca Raton/Fla. 1988, Congr. Numerantium 65, 201-210 (1988).
Review: [For the entire collection see Zbl 665.00002.]
A connected graph G is k-path irregular, k \geq 1, if every two vertices of G that are connected by a path of length k have distinct degrees. This extends the concepts of highly irregular (or 2-path irregular) graphs and totally segregated (or 1-path irregular) graphs. Various sets S of positive integers are considered for which there exist k-path irregular graphs for every k in S. It is shown for every graph G and every odd positive integer k that G can be embedded as an induced subgraph in a k-path irregular graph. Some open problems are also stated.
Classif.: * 05C38 Paths and cycles
05C99 Graph theory
Keywords: k-path irregular graphs
Citations: Zbl 665.00002
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