A sharp inequality involving the psi function.
A sharp upper bound for the spectral radius of a nonnegative matrix and applications
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences.
A short proof of a partion relation for triples.
A short proof of a series evaluation in terms of harmonic numbers.
A short proof of a theorem of Kano and Yu on factors in regular graphs.
A short proof of an identity of Sylvester.
A short proof of rigidity of convex polytopes.
A short proof of the rook reciprocity theorem.
A short WZ-style proof of Abel's identity.
A shorter proof of the distance energy of complete multipartite graphs
Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities...
A simple algorithm for constructing Szemerédi's regularity partition.
A Simple and Relatively Efficient Triangulation of the n-Cube.
A simple bijection between binary trees and colored ternary trees.
A simple card guessing game revisited.
A simple characterization of sets satisfying the central sets theorem.
A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs.
A simple linear algorithm for the connected domination problem in circular-arc graphs
A connected dominating set of a graph G = (V,E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F|) time.
A simple method for constructing small cubic graphs of girths 14, 15, and 16.
A simple method for estimating the bounds of spectral radius of nonnegative irreducible matrices.