An upper bound on algebraic connectivity of graphs with many cutpoints.
An upper bound on the basis number of the powers of the complete graphs
The basis number of a graph is defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. MacLane showed that a graph is planar if and only if its basis number is . Schmeichel proved that the basis number of the complete graph is at most . We generalize the result of Schmeichel by showing that the basis number of the -th power of is at most .
An upper bound on the domination number of a graph.
An upper bound on the Laplacian spectral radius of the signed graphs
In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
An upper estimate of the number of edges of a hypergraph with given diameter
Analoga of Menger's theorem for polar and polarized graphs
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur
Analogues of cliques for oriented coloring
We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.
Analogues of up-down permutations for colored permutations.
Analyse hiérarchique des préférences et généralisations de la transitivité
Analysis of a class of graph partitioning problems
Analysis of an algorithm to construct Fibonacci partitions
Analysis of an asymmetric leader election algorithm.
Analysis of PBIB Designs Using Association Matrices.
Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae
Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...
Analysis of straightening formula.
Analytic aspects of the circulant Hadamard conjecture
We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here these questions,...
Analytic Formulas for Full Steiner Trees.
Analytical enumeration of circulant graphs with prime-squared number of vertices.
Analyzing sets of phylogenetic trees using metrics
The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split metric, which...