Abstract | ||
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A perfect matching in a graph G is a set of nonadjacent edges covering every vertex of G. Motivated by recent progress on the relations between the eigenvalues and the matching number of a graph, in this paper, we aim to present a distance spectral radius condition to guarantee the existence of a perfect matching. Let G be an n-vertex connected graph where n is even and lambda(1) (D(G)) be the distance spectral radius of G. Then the following statements are true.(I) If 4 <= n <= 8 and lambda(1) (D(G)) <= lambda(1 )(D(S-n,S-n/2 -1)), then G contains a perfect matching unless G congruent to S-n,( n/2 -1) where S-n,S- n/2 -1 congruent to K-n(/2-1) boolean OR (n/2 +1)K-1.(II) If n >= 10 and lambda(1) (D(G)) <= lambda(1) D(G*)), then G contains a perfect matching unless G congruent to G* where G* congruent to K-1 boolean OR (Kn-3 boolean OR K-1).Moreover, if G is a connected 2n-vertex balanced bipartite graph with lambda(1) (D(G)) <= lambda(1) (D(B-n-1,B-n-2)), then G contains a perfect matching, unless G congruent to B-n-1,B-n-2 where B-n-1,B-n-2 is obtained from K-n,K-n-2 by attaching two pendent vertices to a vertex in the n-vertex part. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
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2021 | 10.1016/j.dam.2021.08.008 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Distance spectral radius, Perfect matching | Journal | 304 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Yuke Zhang | 1 | 0 | 0.68 |
Huiqiu Lin | 2 | 34 | 11.56 |