منابع مشابه
Unimodular integer circulants
We study families of integer circulant matrices and methods for determining which are unimodular. This problem arises in the study of cyclically presented groups, and leads to the following problem concerning polynomials with integer coefficients: given a polynomial f(x) ∈ Z[x], determine all those n ∈ N such that Res(f(x), xn − 1) = ±1. In this paper we describe methods for resolving this prob...
متن کاملLine Graphs and Circulants
The line graph of G, denoted L(G), is the graph with vertex set E(G), where vertices x and y are adjacent in L(G) iff edges x and y share a common vertex in G. In this paper, we determine all graphs G for which L(G) is a circulant graph. We will prove that if L(G) is a circulant, then G must be one of three graphs: the complete graph K4, the cycle Cn, or the complete bipartite graph Ka,b, for s...
متن کاملOn CIS circulants
A circulant is a Cayley graph over a cyclic group. A well-covered graph is a graph in which all maximal stable sets are of the same size α = α(G), or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. It is not difficult to show that a circulant G is a CIS graph if and only if G and its complement G are both well-co...
متن کاملCirculants and Sequences
A graph G is stable if its normalized chromatic difference sequence is equal to the normalized chromatic di erence sequence of G G, the Cartesian product of G with itself. Let be the independence number of G and ! be its clique number. Suppose that G has n vertices. We show that the rst ! terms of the normalized chromatic di erence sequence of a stable graph G must be =n; and further that if G ...
متن کاملClassifying Arc-Transitive Circulants
A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.
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ژورنال
عنوان ژورنال: The KIPS Transactions:PartA
سال: 2008
ISSN: 1598-2831
DOI: 10.3745/kipsta.2008.15-a.1.27