Signless Laplacian spectral radius and Hamiltonicity of graphs with large minimum degree

Abstract

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to determine the Hamiltonicity of graphs.

A tight $Q$-index condition for a graph to be $k$-path-coverable involving minimum degree

“…For this problem, Fiedler and Nikiforov [12] obtained tight sufficient conditions for graphs to be hamiltonian or traceable. This motivates further study for such question, see [10,9,12,37,21,24,25,35,22,36,28].…”

Sufficient conditions for hamiltonian properties of graphs

“…The most recent result in this area that we are aware of is the following result due to Li et al [40]. [40]).…”

“…The most recent result in this area that we are aware of is the following result due to Li et al [40]. [40]). Let k > 1 be an integer, let n ≥ k 4 + k 3 + 4k 2 + k + 6, and let G be a connected graph of order n with δ…”

“…This result involves the two exceptional classes 1 (n, k) and 1 (n, k) that we will not define here. We refer the interested reader to [40] for the definitions.…”

“…Recently, by involving the minimum degree of the graph as a new parameter, Li and Ning [41,42] extended some of the hamiltonicity results in [25,46,53]. Their results were in turn further improved by Nikiforov [52], Chen et al [10], Ge et al [26], and Li et al [40]. We omit the details since we focus on Hamilton-connectivity instead of hamiltonicity in this chapter.…”