On derangement polynomials of type .
On descents in standard Young tableaux.
On detectable colorings of graphs
Let be a connected graph of order and let be a coloring of the edges of (where adjacent edges may be colored the same). For each vertex of , the color code of with respect to is the -tuple , where is the number of edges incident with that are colored (). The coloring is detectable if distinct vertices have distinct color codes. The detection number of is the minimum positive integer for which has a detectable -coloring. We establish a formula for the detection...
On determination of a cyclic order
On determining minimal spectrally arbitrary patterns.
On determining paint by numbers puzzles with nonunique solutions.
On Difference Matrices, Resolvable Transversal Designs and Generalized Hadamard Matrices.
On difference sets of sets of integers
On difference sets of sets of positive integers
On digraphs with non-derogatory adjacency matrix.
On directed triangles in digraphs.
On disjoint arithmetic progressions
On dissections of the n-cube
On distance edge colourings of a cyclic multigraph
On distance local connectivity and vertex distance colouring
In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
On distances and metrics in discrete ordered sets
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the...
On distances between isomorphism classes of graphs
In 1986, Chartrand, Saba and Zou [3] defined a measure of the distance between (the isomorphism classes of) two graphs based on 'edge rotations'. Here, that measure and two related measures are explored. Various bounds, exact values for classes of graphs and relationships are proved, and the three measures are shown to be intimately linked to 'slowly-changing' parameters.
On distances in some bipartite graphs.
On distinguishing and distinguishing chromatic numbers of hypercubes
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number of G. Extending these concepts to infinite graphs we prove that and , where denotes the hypercube of countable dimension. We also show that , thereby completing the investigation of finite hypercubes with respect to . Our results...
On divisibility of Narayana numbers by primes.