Abstract
A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.
Highlights
E adjacency matrix of G of order n is the matrix A(G) [aij] of order n, where aij 1 if vi is adjacent to vj and aij 0 otherwise
Denote by q(G) the signless Laplacian spectral radius of G, which is the largest eigenvalue of Q(G)
A graph G is pancyclic if it contains all l− cycle, 3 ≤ l ≤ n
Summary
E adjacency matrix of G of order n is the matrix A(G) [aij] of order n, where aij 1 if vi is adjacent to vj and aij 0 otherwise. Denote by q(G) the signless Laplacian spectral radius of G, which is the largest eigenvalue of Q(G). In 2010, Fiedler and Nikiforov [3] first gave sufficient conditions for the given graph to be Hamiltonian (or traceable) in terms of the spectral radius of the graph. It provides an easy and efficient determination method. G8 is the graph obtained from K2 ∨ 2K1 by adding one pedending edge on two vertexes of degree 3, respectively
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