On a functional-difference equation of Runyon, Morrison, Carlitz, and Riordan.
On a generalization of binomial coefficients. (Sur une généralisation des coefficients binomiaux.)
On a generalization of duality triads
Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.
On a generalization of Meyniel's conjecture on the Cops and Robbers game.
On a generalization of perfect -matching
The paper is concerned with the existence of non-negative or positive solutions to , where is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.
On a generalization of the friendship theorem
The Friendship Theorem states that if any two people, of a group of at least three people, have exactly one friend in common, then there is always a person who is everybody's friend. In this paper, we generalize the Friendship Theorem to the case that in a group of at least three people, if every two friends have one or two common friends and every pair of strangers have exactly one friend then there exist one person who is friend to everybody in the group. In particular, we show that the graph...
On a generalization of the matroid
On a generalization of the Narayana triangle.
On a generalized recurrence for Bell numbers.
On a graph invariant related to the sum of all distances in a graph.
On a graph theory problem of M. Koman
On a Graph Transformation That Preserves the Stability Number
On a Hamiltonian cycle of the fourth power of a connected graph
In this paper the following theorem is proved: Let be a connected graph of order and let be a matching in . Then there exists a hamiltonian cycle of such that .
On a local property of the unoriented graph of a modular multilattice
On a matching distance between rooted phylogenetic trees
The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs, the values...
On a maximal distance between graphs
On a minimum cycle basis of a graph
On a multiplicative partition function.
On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem
Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube...
On a new family of generalized Stirling and Bell numbers.