Path extendable graphs
type: Item
instance of: scholarly article
title: Path extendable graphs
zbMATH Open document ID: 0729.05027
DOI: 10.1007/BF02651089
published in: Periodica Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: A path P in graph G is extendable if there exists a path \(P'\) in G with the same endvertices as P and the vertex set of \(P'\) consists of V(P) together with one additional vertex. A graph is path extendable if every non-Hamiltonian path in G is extendable. Graph G is fully path extendable if it is extendable and has diameter at most two. A graph is panconnected if for each pair of vertices u, v, there exists a u-v path of length 1 for each integer 1, d(u,v)\(\leq 1\leq p-1\). A graph G is PLD-maximal if for each 1, \(2\leq 1\leq p-1\) there exists a path of length 1 connecting each pair of distance vertices of G. It follows immediately that every path extendable graph is panconnected and every fully path extendable graph is PLD-maximal. In this paper sufficient conditions for a graph to be path extendable or fully path extendable are investigated.
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 4204374
zbMATH Keywords: fully path extendable
zbMATH Keywords: panconnected
zbMATH Keywords: PLD-maximal
author: George R. T. Hendry
reviewed by: John Mitchem
MaRDI profile type: Publication
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cites work: Q5728984
full work available at URL: https://doi.org/10.1007/bf02651089
OpenAlex ID: W1975564488
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description: scientific article; zbMATH DE number 4204374