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An upper bound of a generalized upper Hamiltonian number of a graph

Martin Dzúrik (2021)

Archivum Mathematicum

In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph H we define the H -Hamiltonian number of a graph G . We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs G and H using H -Hamiltonian number of G . Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper H -Hamiltonian...

An upper bound of the basis number of the strong product of graphs

Mohammed M.M. Jaradat (2005)

Discussiones Mathematicae Graph Theory

The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper we give an upper bound of the basis number of the strong product of a graph with a bipartite graph and we show that this upper bound is the best possible.

An upper bound on the basis number of the powers of the complete graphs

Salar Y. Alsardary (2001)

Czechoslovak Mathematical Journal

The basis number of a graph G is defined by Schmeichel to be the least integer h such that G has an h -fold basis for its cycle space. MacLane showed that a graph is planar if and only if its basis number is ≤ 2 . Schmeichel proved that the basis number of the complete graph K n is at most 3 . We generalize the result of Schmeichel by showing that the basis number of the d -th power of K n is at most 2 d + 1 .

An upper bound on the Laplacian spectral radius of the signed graphs

Hong-Hai Li, Jiong-Sheng Li (2008)

Discussiones Mathematicae Graph Theory

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.

Analogues of cliques for oriented coloring

William F. Klostermeyer, Gary MacGillivray (2004)

Discussiones Mathematicae Graph Theory

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.

Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae

I.V. Rudskiy, G.E. Titova, T.B. Batygina (2010)

Mathematical Modelling of Natural Phenomena

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...

Analyzing sets of phylogenetic trees using metrics

Damian Bogdanowicz (2011)

Applicationes Mathematicae

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...

Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view

Luis M. Torres, Annegret K. Wagler (2013)

RAIRO - Operations Research - Recherche Opérationnelle

To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.

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