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25 papers · 2 filters
The generalized connectivity of complete bipartite graphs
Shasha Li, Wei Li, Xueliang Li
Let be a nontrivial connected graph of order , and an integer with . For a set of vertices of , let denote the maximum number of…
Rainbow connection numbers of complementary graphs
Xueliang Li, Yuefang Sun
A path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph is rai…
Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees
William Y. C. Chen, Louis W. Shapiro, Susan Y. J. Wu
The lattice polynomials are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point . In particular, $L_{2n, n…
Complete solution to a conjecture on the maximal energy of unicyclic graphs
Bofeng Huo, Xueliang Li, Yongtang Shi
For a given simple graph , the energy of , denoted by , is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let be the…
Minimal Permutations and 2-Regular Skew Tableaux
William Y. C. Chen, Cindy C. Y. Gu, Kevin J. Ma
Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let de…
Arithmetic Properties of Overpartition Pairs
William Y. C. Chen, Bernard L. S. Lin
Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of , the number of overpartition pairs of n. In part…