Propagation of mean degrees.
Proper connection number of bipartite graphs
An edge-colored graph is proper connected if every pair of vertices is connected by a proper path. The proper connection number of a connected graph , denoted by , is the smallest number of colors that are needed to color the edges of in order to make it proper connected. In this paper, we obtain the sharp upper bound for of a general bipartite graph and a series of extremal graphs. Additionally, we give a proper -coloring for a connected bipartite graph having and a dominating cycle...
Properties determined by the Ihara zeta function of a graph.
Properties of digraphs connected with some congruence relations
The paper extends the results given by M. Křížek and L. Somer, On a connection of number theory with graph theory, Czech. Math. J. 54 (129) (2004), 465–485 (see [5]). For each positive integer define a digraph whose set of vertices is the set and for which there is a directed edge from to if The properties of such digraphs are considered. The necessary and the sufficient condition for the symmetry of a digraph is proved. The formula for the number of fixed points of is established....
Properties of the Steiner triple systems of order 19.
Properties of the van der Pol numbers and polynomials.
Propriétés arithmétiques des polynômes d'Euler
Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci
Nous étudions certaines propriétés combinatoires, ergodiques et arithmétiques du point fixe de la substitution de Tribonacci (introduite par G. Rauzy) et de la rotation du tore qui lui est associée. Nous établissons une généralisation géométrique du théorème des trois distances et donnons une formule explicite pour la fonction de récurrence du point fixe. Nous donnons des propriétés d’approximation diophantienne du vecteur de la rotation de : nous montrons, que pour une norme adaptée, la suite...
Propriétés des diagrammes de Cayley
Propriétés nouvelles des tableaux de Young
Průměr grafu pologrupy
Průměr grafu systému vlastních podpologrup komutativní pologrupy
Pruning Galton–Watson trees and tree-valued Markov processes
We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process by pruning Galton–Watson trees and an analogous process by pruning a critical or subcritical Galton–Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process run until its ascension time has a representation in terms of . A similar result was obtained by Aldous and...
Pseudodual grids and extensions of generalized quadrangles.
Pure circuits in cube graphs
p-Wiener intervals and p-Wiener free intervals
A positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n(≠ 2,5) is Wiener graphical. For any positive integer p, an interval [a,b] is said to be a p-Wiener interval if for each positive integer n ∈ [a,b] there exists a graph G on p vertices such that W(G) = n. For any positive integer p, an interval [a,b] is said to be p-Wiener free interval (p-hyper-Wiener free interval) if there exist no graph G on p...