Energy Conditions for Hamiltonicity of Graphs

Abstract EN

Let G be an undirected simple graph of order n.

Let A(G) be the adjacency matrix of G, and let μ1(G)≤μ2(G)≤⋯≤μn(G) be its eigenvalues.

The energy of G is defined as ℰ(G)=∑i=1n|μi(G)|.

Denote by GBPT a bipartite graph.

In this paper, we establish the sufficient conditions for G having a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement of G, and give the sufficient condition for GBPT having a Hamiltonian cycle in terms of the energy of the quasi-complement of GBPT.