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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 669.05046

**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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