Kavli Affiliate: Ke Wang
| First 5 Authors: Fengyun Ren, Shumin Zhang, Ke Wang, ,
| Summary:
The ${K_{1,1}, K_{1,2},C_m: mgeq3}$-factor of a graph is a spanning
subgraph whose each component is an element of ${K_{1,1}, K_{1,2},C_m:
mgeq3}$. In this paper, through the graph spectral methods, we establish the
lower bound of the signless Laplacian spectral radius and the upper bound of
the distance spectral radius to determine whether a graph admits a
${K_2}$-factor. We get a lower bound on the size (resp. the spectral radius)
of $G$ to guarantee that $G$ contains a ${K_{1,1}, K_{1,2},C_m:
mgeq3}$-factor. Then we determine an upper bound on the distance spectral
radius of $G$ to ensure that $G$ has a ${K_{1,1}, K_{1,2},C_m:
mgeq3}$-factor. Furthermore, by constructing extremal graphs, we show that
the above all bounds are best possible.
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