TITLE

The Asymmetry Number of Finite Tournaments, and Some Related Results

AUTHOR(S)
Satake, Shohei
PUB. DATE
November 2017
SOURCE
Graphs & Combinatorics;Nov2017, Vol. 33 Issue 6, p1433
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We introduce the concept of asymmetry number for finite tournaments, as a natural generalization of that for graphs by Erdős and Rényi (Acta Math Acad Sci Hungar 14:295-315, 1963). We prove an upper bound for the asymmetry number of finite tournaments and discuss its asymptotically best possibility. We also give an alternative proof of a theorem by Jaligot and Khelif (Aequat Math 67:73-79, 2004) which states that the random tournament can be expressed by a Cayley tournament on an arbitrary countable group without involutions. We slightly improve a result by Cameron and Johnson (Math Proc Camb Philos Soc 102:223-231, 1987).
ACCESSION #
126308061

 

Related Articles

  • Suborbits in Infinite Primitive Permutation Groups. Evans, David M. // Bulletin of the London Mathematical Society;Oct2001, Vol. 33 Issue 5, p583 

    For every infinite cardinal κ, we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann. 2000 Mathematics Subject Classification 20B07, 20B15, 03C50, 05C20.

  • Edge-symmetric distance-regular covers of cliques: Affine case. Makhnev, A.; Paduchikh, D.; Tsiovkina, L. // Doklady Mathematics;Mar2013, Vol. 87 Issue 2, p224 

    The article presents a study which considers undirected graphs with no loops or multiple edges in a given subset of automorphism with a set of fixed vertices under any automorphisms on the function and value of X as a subset. It refers to the definition of a quotient through an assumption that...

  • Edge-symmetric semitriangular Higman graphs. Zyulyarkina, N.; Makhnev, A. // Doklady Mathematics;Nov2014, Vol. 90 Issue 3, p701 

    The article presents a mathematical research which discusses the classification of edge-symmetric semi-triangular Higman graphs. Information about the definition of an edge-symmetric graph, vertices and parameters, and the role of automorphism group is discussed. Also mentioned are details on...

  • Study on necessary and sufficient conditions for Euler graph and Hamilton graph. Yan Cui; Chao-Dong Cui // Advanced Materials Research;2014, Issue 1044-1046, p1357 

    Three theorems are proposed in this paper. The first theorem is that a connected undirected graph G is an Euler graph if and only if G can be expressed as the union of two circles without overlapped sides. Namely, equation E(c1E ) + E(c2E ) = E(G) satisfies. The second theorem is that a...

  • THE GROUP OF AUTOMORPHISMS OF THE LATTICE OF FUZZY TOPOLOGIES. Chacko, Baby // Far East Journal of Mathematical Sciences;Jan2013, Vol. 72 Issue 1, p79 

    The set of all L-fuzzy topologies on a nonempty set X denoted by LFT(X , L), where L is the membership lattice, is a complete lattice under the partial order of set inclusion. In this paper, we characterize the group of automorphisms of the lattice LFT(X , L) when L = {0, 1 2, 1} under usual order.

  • An automorphism group of a distance-regular graph with intersection array {24, 21, 3; 1, 3, 18}. Makhnev, A.; Paduchikh, D. // Algebra & Logic;Sep2012, Vol. 51 Issue 4, p319 

    We study automorphisms of a hypothetical distance-regular graph with intersection array {24 , 21 , 3; 1 , 3 , 18} .

  • The Socle of Automorphism Groups of Linear Spaces. Camina, Alan R. // Bulletin of the London Mathematical Society;1996, Vol. 28 Issue 3, p269 

    The article examines the socle of a point-primitive line-transitive automorphism group of a linear space. It presents a theorem to show the results and provides an explanation on the situation when the socle is an alternating group. It mentions that there have various contributions to the...

  • A criterion for the elementary equivalence of endomorphism rings and automorphism groups of Abelian p-groups. Bunina, E.; Mikhalev, A.; Roizner, M. // Doklady Mathematics;Aug2014, Vol. 90 Issue 1, p399 

    The article discusses topics such as endomorphism rings, automorphism groups and Abelian groups. Other topics include Baer-Kaplansky theorem, isomorphic groups and predicate variables. Relationship between properties of Abelian groups and mathematical models are discussed. Several mathematical...

  • TREE-LIKE PARTIAL HAMMING GRAPHS. GOLOGRANC, TANJA // Discussiones Mathematicae: Graph Theory;2014, Vol. 34 Issue 1, p137 

    Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a...

  • Trivial Cycles in Graphs Embedded in 3-Manifolds. Wu, Ying-Qing // Bulletin of the London Mathematical Society;1996, Vol. 28 Issue 2, p190 

    A cycle C of a graph Γ embedded in a 3-manifold M is said to be trivial in Γ if it bounds a disk with interior disjoint from Γ. Let e be an edge of Γ with ends on C. We shall study the relation between triviality of cycles in Γ and that of Γ − e and Γ/e. Let C1...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics