# THE CAUCHY-SCHWARZ INEQUALITY IN CAYLEY GRAPH AND TOURNAMENT STRUCTURES ON FINITE FIELDS

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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...

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This paper investigates the role of pictures in mathematics in the particular case of Cayley graphsï¿½the graphic representations of groups. I shall argue that their principal function in that theoryï¿½to provide insight into the abstract structure of groupsï¿½is 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 â‰¥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product (â„¤/2)â‰€Î“, where Î“ = *â„¤/2 is the free product group of q factors â„¤/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...