Graphs uniquely Hamiltonian-connected from a vertex
type: Item
instance of: scholarly article
title: Graphs uniquely Hamiltonian-connected from a vertex
zbMATH Open document ID: 0535.05043
DOI: 10.1016/0012-365X(84)90151-1
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A graph G is called Hamiltonian-connected from a vertex v of G if G contains a Hamiltonian v-w path for each vertex \(w\neq v\). Such graphs have been studied by \textit{G. Chartrand} and \textit{E. A. Nordhaus} [4th Int. Conf., Kalamazoo/Mich. 1980, 189-201 (1981; Zbl 0471.05052)]. Furthermore if the v-w path is unique for each vertex \(w\neq v\) the author calls it uniquely Hamiltonian-connected from v. He constructs several families of graphs with this property and gives many necessary conditions on it. For example, if G is uniquely Hamiltonian-connected from v, has order n, \(n\geq 3\), then n is odd, the degree of v is even and G has at most (3n-3)/2 edges. Despite these results such graphs are not characterized and the author asks many questions about them.
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 3849271
zbMATH Keywords: Hamiltonian path
zbMATH Keywords: Hamiltonian connected
author: George R. T. Hendry
MaRDI profile type: Publication
cites work: Q5564134
cites work: Q3924248
cites work: Parallel concepts in graph theory
cites work: Hamilton connected graphs
cites work: Hamiltonian Cycles and Uniquely Edge Colourable Graphs
description: scientific article; zbMATH DE number 3849271