6 papers · 1 filter
Signless Laplacian index conditions for trebly chorded cycles in graphs with given order
Jin Cai, Bo Zhou
It is proved that for a graph of order , where , if the signless Laplacian index is larger than or equal to certain value depending on , then the graph contains a tre…
Extremal -index problem in outerplanar graphs
Jin Cai, Leyou Xu, Bo Zhou
Outerplanar Turán problem has received considerable attention recently. We study the spectral version via -index. We determine the unique graph that maximizes the -index amon…
Eigenvalue conditions implying edge-disjoint spanning trees and a forest with constraints
Jin Cai, Bo Zhou
Let be a nontrivial graph with minimum degree and an integer with . In the literature, there are eigenvalue conditions that imply contains edge-disjoint…
Spectral conditions for the existence of chorded cycles in graphs with fixed size
Jin Cai, Leyou Xu, Bo Zhou
A chorded cycle is a cycle with at least one chord. Gould asked in [Graphs Comb. 38 (2022) 189] the question: What spectral conditions imply a graph contains a chorded cycle? For a…
Spectral conditions for graphs in which every edge belongs to a factor
Jin Cai, Bo Zhou
A factor of a graph is a spanning subgraph. Spectral sufficient conditions are provided via spectral radius and signless Laplacian spectral radius for graphs with (i) a matching of…
Spectral conditions for factor-criticality of graphs
Jin Cai, Bo Zhou
A graph is -factor-critical if has a perfect matching for any -subset of the vertex set of . In this paper, we investigate the factor-criticality of graphs w…