On pancyclic line graphs
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.)
scientific article; zbMATH DE number 4049681
scientific article