A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications.
A refinement of Cayley's formula for trees.
A refinement of the formula for -ary trees and the Gould-Vandermonde's convolution.
A reformulation of matrix graph grammars with Boolean complexes.
A regular graph of girth 6 and valency 11.
A relation between restricted and unrestricted weighted Motzkin paths.
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.
A relationship between the major index for tableaux and the charge statistic for permutations.
A relative Laplacian spectral recursion.
A remark about fractional -critical graphs.
A remark on almost Moore digraphs of degree three.
A remark on branch weights in countable trees
Let be a tree, let be its vertex. The branch weight of is the maximum number of vertices of a branch of at . The set of vertices of in which attains its minimum is the branch weight centroid of . For finite trees the present author proved that coincides with the median of , therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.
A remark on cancellation in direct products of graphs
A remark on distances in products of graphs
A Remark On Filter Regularity
A remark on filter regularity.
A remark on graph operators
A theorem is proved which implies affirmative answers to the problems of E. Prisner. One problem is whether there are cycles of the line graph operator with period other than 1, the other whether there are cycles of the 4-edge graph operator with period greater than 2. Then a similar theorem follows.
A remark on isotopies of digraphs and permutation matrices
A remark on self-centroidal graphs
A remark on signed posets and signed graphs