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On some third parts of nearly complete digraphs

Mariusz Meszka, Zdzisław Skupień
2000 Discrete Mathematics  
It is proved that some self-converse digraphs are not among the near-third parts of the complete digraph DK 5 in four of the six possible cases.  ...  For n = 9 + 6k; k = 0; 1; : : : ; a third part D of DKn is found such that D is a self-converse oriented graph and all D-decompositions of DKn have trivial automorphism group.  ...  For n = 5; there is no ceiling third part of the complete digraph DK 5 which could be a self-converse oriented graph. Remark 2.  ... 
doi:10.1016/s0012-365x(99)00214-9 fatcat:ardt5tmhrjawromujsinkuggi4

Decompositions of nearly complete digraphs into t isomorphic parts

Mariusz Meszka, Zdzisław Skupień
2009 Discussiones Mathematicae Graph Theory  
Two sets of nearly tth parts are constructively proved to be nonempty.  ...  An arc decomposition of the complete digraph DK n into t isomorphic subdigraphs is generalized to the case where the numerical divisibility condition is not satisfied.  ...  Acknowledgement The research was supported by the Ministry of Science and Information Society Technologies of the Republic of Poland, Grant No. 1 P03A 037 27.  ... 
doi:10.7151/dmgt.1464 fatcat:jor3dk5wavc4ji2olf65zqgwfq

Page 7619 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
It is proved that some self-converse digraphs are not among the near-third parts of the complete digraph Z Ks in four of the six possible cases.  ...  Summary: “For the complete digraph 9 K,, with n > 3, its half and its third (or near-third) part, both non-self-converse, are exhibited.  ... 

Page 5326 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
(PL-STSAM; Krakow) Self-converse and oriented graphs among the third parts of nearly complete digraphs. (English summary) Combinatorica 18 (1998), no. 3, 413-424.  ...  The existence of nearly third parts which are oriented and/or self- converse digraphs is settled in the affirmative for all or most n’s.  ... 

An application of neighbourhoods in digraphs to the classification of binary dynamics [article]

Pedro Conceição, Dejan Govc, Jānis Lazovskis, Ran Levi, Henri Riihimäki, Jason P. Smith
2021 arXiv   pre-print
The central object of study in this article is the closed neighbourhood of a vertex v in a graph 𝒢, namely the subgraph of 𝒢 that is induced by v and all its neighbours in 𝒢.  ...  Allowing time to vary and recording the spiking patterns of the neurons in the network produces an example of binary dynamics on the encoding graph, namely a one-parameter family of binary states on it  ...  The authors wish to thank Michael Reimann of the Blue Brain Project for supporting this project and sharing his wisdom and knowledge with us, and Daniela Egas Santander for suggestions to advance our ideas  ... 
arXiv:2104.06519v3 fatcat:okccvjltyrbcpl2734hg6axjji

Charge distribution as a tool to investigate structural details. III. Extension to description in terms of anion-centred polyhedra

Jean-Guillaume Eon, Massimo Nespolo
2015 Acta Crystallographica. Section B: Structural Science, Crystal Engineering and Materials  
A graph-theoretical description of the structures rationalizes and gives further support to the conclusions obtainedviathe CHARDI approach.  ...  The charge distribution (CHARDI) method is a self-consistent generalization of Pauling's concept of bond strength which does not make use of empirical parameters but exploits the experimental geometry  ...  In this third part we present a further extension, to anioncentred polyhedra.  ... 
doi:10.1107/s2052520614027048 pmid:25643714 fatcat:gmpqzptzk5gwhpkqvahcurd3v4

Cayley–Abels graphs and invariants of totally disconnected, locally compact groups [article]

Arnbjörg Soffía Árnadóttir
2021 arXiv   pre-print
Define the minimal degree of G as the minimal degree of a Cayley–Abels graph of G.  ...  We relate the minimal degree in various ways to the modular function, the scale function and the structure of compact open subgroups.  ...  Conversely, part of this work was completed when the second author was visiting George Willis at The University of Newcastle in spring 2020.  ... 
arXiv:2105.12630v1 fatcat:5bt3wevdjjco5jwdjod6x6a24e

International Journal Of Mathematical Combinatorics, Vol.4 [article]

Mao, Linfan (Editor-in-Chief)
2010 Zenodo  
The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising  ...  geometry and topology and their applications to other sciences.  ...  Some of them are analogous to those of the signed domatic number in [5] and studied sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.  ... 
doi:10.5281/zenodo.8808 fatcat:fsjaqcxutrfajefimgl54db4ri

Ring cohesion theory in marriage and social networks

Douglas R. White
2004 Mathématiques et sciences humaines  
Wiener (1948) ; The Mathematical Theory of Communication, de C. Shannon and W.  ...  sciences, the indirect outcome of modern developments in mathematics which have given increasing importance to the qualitative point of view in contradistinction to the quantitative point of view of traditional  ...  The first presentation of the ideas of ring cohesion theory in summer 2003 benefited from support of the Santa Fe Institute for the annual ISCOM meeting.  ... 
doi:10.4000/msh.2940 fatcat:opegafkkhbcmno63wl5urss3am

A SURVEY OF PROGRESS IN GRAPH THEORY IN THE SOVIET UNION

James Turner, William H. Kautz
1970 Annals of the New York Academy of Sciences  
A complete bibliography is given at tIhe end of the report. ti CONTENTS ABSTRACT .  ...  Very littlv Soviet work has been reported on connectivity propertieb of graphs, matroid theory, the exact enumeration of graphs having prescribed properties, isomorphism testing, graph coloring, and the  ...  more nearly characterize the graph.  ... 
doi:10.1111/j.1749-6632.1970.tb56496.x fatcat:cbb5x22w2farrnw5sijyovn66i

Ranking hubs and authorities using matrix functions [article]

Michele Benzi, Ernesto Estrada, Christine Klymko
2012 arXiv   pre-print
The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks.  ...  We explicitly determine the exponential of this adjacency matrix in terms of the adjacency matrix of the original, directed network, and we give an interpretation of centrality and communicability in this  ...  We are indebted to Tammy Kolda (Sandia National Laboratories) and David Gleich (Purdue University) for valuable suggestions.  ... 
arXiv:1201.3120v3 fatcat:e4qwzam5ebg5tfogweleg6fulm

Matching theory—a sampler: from Dénes König to the present

Michael D. Plummer
1992 Discrete Mathematics  
., Matching theory-a sampler: from D&es Kijnig to the present, Discrete Mathematics 100 (1992) 177-219. *  ...  We would also be remiss did we not thank Pulleyblank for his professional assistance in the presentation and associated 'media show' that accompanied the talk at Hindsgavl which formed the preliminary  ...  and Carsten Thomassen.  ... 
doi:10.1016/0012-365x(92)90640-2 fatcat:4qibuxklhreuxpawcf32lgb47m

Ranking hubs and authorities using matrix functions

Michele Benzi, Ernesto Estrada, Christine Klymko
2013 Linear Algebra and its Applications  
The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks.  ...  We explicitly determine the exponential of this adjacency matrix in terms of the adjacency matrix of the original, directed network, and we give an interpretation of centrality and communicability in this  ...  Acknowledgments We are indebted to Tammy Kolda (Sandia National Laboratories), Stratis Gallopoulos (University of Patras) and David Gleich (Purdue University) for valuable suggestions.  ... 
doi:10.1016/j.laa.2012.10.022 fatcat:6ejn4p6r7rd67devtihh5exrya

Automated Bifurcation Analysis for Nonlinear Elliptic Partial Difference Equations on Graphs [article]

John M. Neuberger and Nandor Sieben and James W. Swift
2010 arXiv   pre-print
Region wherein we present some of our recent advances concerning symmetry, bifurcation, and automation fo We apply the symmetry analysis found in the SIAM paper to arbitrary graphs in order to obtain  ...  We seek solutions u∈^n to the semilinear elliptic partial difference equation -Lu + f_s(u) = 0, where L is the matrix corresponding to the Laplacian operator on a graph G and f_s is a one-parameter family  ...  We have a counterexample which shows that the converse of Proposition 2.1 is false.  ... 
arXiv:1010.2257v1 fatcat:x3cv72ksejc6fj3beyxfu6s64a

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
each of whom gave a one-hour lecture. The third type of talks were the 20-minute contributed talks running in two parallel sessions and given by 39 speakers.  ...  graph theory and combinatorics.  ...  This work is part of project XTerM, funded with the support from the European Union with the European Regional Development Fund (ERDF) and from the Regional Council of Normandie. Acknowledgements.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby
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