On the degrees of graphs with
On the density of languages representing finite set partitions.
On The Determinant of q-Distance Matrix of a Graph
In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph...
On the determining number and the metric dimension of graphs.
On the diagram of Schröder permutations.
On the diameter of the intersection graph of a finite simple group
Let be a finite group. The intersection graph of is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of , and two distinct vertices and are adjacent if , where denotes the trivial subgroup of order . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection...
On the dichromatic number in kernel theory
On the dimension of additive sets
We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of {0,1}ⁿ ⊂ ℤⁿ.
On the dimer problem and the Ising problem in finite 3-dimensional lattices.
On the discrepancy of coloring finite sets.
On the discrepancy of quasi-progressions.
On the distance function of a connected graph
An axiomatic characterization of the distance function of a connected graph is given in this note. The triangle inequality is not contained in this characterization.
On the distance paired-domination of circulant graphs.
On the distance polynomial of a graph
Several properties of the distance polynomial are discussed.
On the distance spectrum of a cycle
Analytic expressions for the roots of the distance polynomial of a cycle are given.
On the distribution of modulo p
On the distribution of depths in increasing trees.
On the distribution of the number of vertices in layers of random trees.
On the distribution of the -Euler polynomials and the -Genocchi polynomials of higher order.
On the divisibility of generalized central trinomial coefficients.