January 2014
Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p153
Academic Journal
The Cayley graph construction provides a natural grid structure on a finite vector space over a field of prime or prime square cardinality, where the characteristic is congruent to 3 modulo 4, in addition to the quadratic residue tournament structure on the prime subfield. Distance from the null vector in the grid graph defines a Manhattan norm. The Hermitian inner product on these spaces over finite fields behaves in some respects similarly to the real and complex case. An analogue of the Cauchy-Schwarz inequality is valid with respect to the Manhattan norm. With respect to the non-transitive order provided by the quadratic residue tournament, an analogue of the Cauchy-Schwarz inequality holds in arbitrarily large neighborhoods of the null vector, when the characteristic is an appropriate large prime.


Related Articles

  • A Family of Nonnormal Cayley Digraphs. Feng, Yan Quan; Wang, Dian Jun; Chen, Jing Lin // Acta Mathematica Sinica;2001, Vol. 17 Issue 1 

    Abstract We call a Cayley digraph GAMMA = Cay(G, S) normal for G if G[sub R], the right regular representation of G, is a normal subgroup of the full automorphism group Aut(GAMMA) of GAMMA. In this paper we determine the normality of Cayley digraphs of valency 2 on nonabelian groups of order...

  • Fault Tolerance of Cayley Graphs. Gao, Shuhong; Novick, Beth // Annals of Combinatorics;2007, Vol. 11 Issue 2, p161 

    It is a difficult problem in general to decide whether a Cayley graph Cay( G; S) is connected where G is an arbitrary finite group and S a subset of G. For example, testing primitivity of an element in a finite field is a special case of this problem but notoriously hard. In this paper, it is...

  • Why do Mathematicians Need Different Ways of Presenting Mathematical Objects? The Case of Cayley Graphs. Starikova, Irina // Topoi;Apr2010, Vol. 29 Issue 1, p41 

    This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs�the graphic representations of groups. I shall argue that their principal function in that theory�to provide insight into the abstract structure of groups�is performed employing...

  • Algebraic Specification of Interconnection Network Relationships by Permutation Voltage Graph Mappings. Gross, J. L.; Chen, Jianer // Mathematical Systems Theory;1996, Vol. 29 Issue 5, p451 

    Develops algebraic methods for mapping one large graph into another and for measuring some performance-related characteristics of such mappings, as a complement of algorithmic techniques. Guest-host network relationship; Cayley graphs; Group-action graphs; Formulas for the measurement of the...

  • A Geometric Characterization of Automatic Monoids. SILVA, PEDRO V.; STEINBERG, BENJAMIN // Quarterly Journal of Mathematics;Sep2004, Vol. 55 Issue 3, p333 

    It is well known that automatic groups can be characterized using geometric properties of their Cayley graphs. Along the same line of thought, we provide a geometric characterization of automatic monoids. This involves working with a slightly strengthened definition of an automatic monoid which...

  • Rate of escape on the lamplighter tree. Gilch, L. // Journal of Mathematical Sciences;Jan2009, Vol. 156 Issue 1, p173 

    Suppose we are given a homogeneous tree {ie173-01} of degree q ≥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product (ℤ/2)≀Γ, where Γ = *ℤ/2 is the free product group of q factors ℤ/2....

  • On non-normal arc-transitive 4-valent dihedrants. Kov�cs, Istv�n; Kuzman, Bo�tjan; Malnic, Aleksander // Acta Mathematica Sinica;Aug2010, Vol. 26 Issue 8, p1485 

    Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group D n such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within D n. It is shown that X is isomorphic either to the lexicographic product C n[2 K1] with n = 4...

  • On Cayley Graphs of Inverse Semigroups. Kelarev, A. V. // Semigroup Forum;May/Jun2006, Vol. 72 Issue 3, p411 

    We describe all finite inverse semigroups and all commutative inverse semigroups with bipartite Cayley graphs. Examples are given which show that this description does not generalize to arbitrary inverse semigroups. Next, we describe all inverse epigroups with Cayley graphs which are disjoint...

  • D-saturated property of the Cayley graphs of semigroups. Dong Yang; Xing Gao // Semigroup Forum;Jan/Feb2010, Vol. 80 Issue 1, p174 

    Let D be a finite graph. A semigroup S is said to be Cayley D-saturated with respect to a subset T of S if, for all infinite subsets V of S, there exists a subgraph of Cay( S, T) isomorphic to D with all vertices in V. The purpose of this paper is to characterize the Cayley D-saturated property...


Read the Article


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

Try another library?
Sign out of this library

Other Topics