On pancyclic line graphs
type: Item
instance of: scholarly article
title: On pancyclic line graphs
zbMATH Open document ID: 0644.05033
DOI: 10.1007/BF02008367
author: Ronghua Shi
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1987-01-01T00:00:00Z
review text: A graph with n vertices is pancyclic if it contains for every k, \(3\leq k\leq n,\) a circuit of length k. A graph is vertex pancyclic if every vertex is contained in a circuit of length k for every k, \(3\leq k\leq n\). In the paper are given some sufficient conditions for a graph which is a line graph of a finite graph G to be (vertex) pancyclic. 1) If a connected graph G is an edge triangular graph then the line graph L(G) is vertex pancyclic. 2) If G is a graph with n vertices and \(d(x)+d(y)\geq n+1\) for (x,y)\(\in E(G)\) then L(G) is vertex pancyclic. 3) If G is connected with \(n\geq 6\) vertices and \(d(x)+d(y)\geq n-1-p(n)\) for every (x,y)\(\in E(G)\) then L(G) is pancyclic. \((p(n)=0\) for n even, \(p(n)=1\) for n odd.)
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 4049681
zbMATH Keywords: pancyclic graph
zbMATH Keywords: line graph
reviewed by: Ludovit Niepel
MaRDI profile type: Publication
cites work: Locally connected graphs
cites work: Every connected, locally connected nontrivial graph with no induced claw is hamiltonian
cites work: On hamiltonian line graphs
cites work: On Eulerian and Hamiltonian Graphs and Line Graphs
full work available at URL: https://doi.org/10.1007/bf02008367
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description: scientific article; zbMATH DE number 4049681