The spanning <i>k</i>-trees, perfect matchings and spectral radius of graphs
Dandan Fan, Sergey Goryainov, Xueyi Huang, Huiqiu Lin
Abstract
A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed order and minimum degree.
Topics & Concepts
CombinatoricsSpectral radiusMathematicsBipartite graphSpanning treeVertex (graph theory)Adjacency listDiscrete mathematicsMatching (statistics)Minimum degree spanning treeGraphEigenvalues and eigenvectorsPhysicsStatisticsQuantum mechanicsGraph theory and applicationsAdvanced Graph Theory ResearchMatrix Theory and Algorithms