9 research outputs found
Stability number and f-factors in graphs
We present a new sufficient condition on stability number and toughness of
the graph to have an f-factor
Sufficient conditions for fractional [a,b]-deleted graphs
Let and be two positive integers with , and let be a
graph with vertex set and edge set . Let
be a function. If holds for every
, then the subgraph of with vertex set and edge set
, denoted by , is called a fractional -factor of with
indicator function , where denotes the set of edges incident with
in and . A graph is defined as a
fractional -deleted graph if for any , contains a
fractional -factor. The size, spectral radius and signless Laplacian
spectral radius of are denoted by , and ,
respectively. In this paper, we establish a lower bound on the size, spectral
radius and signless Laplacian spectral radius of a graph to guarantee that
is a fractional -deleted graph.Comment: 1
Spanning k-trees and distance spectral radius in graphs
Let be an integer. A tree is called a -tree if
for each , that is, the maximum degree of a -tree is at most .
Let denote the distance spectral radius in , where
denotes the distance matrix of . In this paper, we verify a upper bound for
in a connected graph to guarantee the existence of a
spanning -tree in .Comment: 11 page
Signless Laplacian spectral radius for a k-extendable graph
Let and be two nonnegative integers with (mod 2), and let
be a graph of order with a 1-factor. Then is said to be
-extendable for if every matching in of size
can be extended to a 1-factor. In this paper, we first establish a lower
bound on the signless Laplacian spectral radius of to ensure that is
-extendable. Then we create some extremal graphs to claim that all the
bounds derived in this article are sharp.Comment: 11 page