Orthogonal systems in finite graphs

نویسندگان

  • Andrew J. Duncan
  • Ilya V. Kazachkov
  • Vladimir N. Remeslennikov
چکیده

Let Γ be a finite graph and GΓ be the corresponding free partially commutative group. In this paper we construct orthogonality theory for graphs and free partially commutative groups. The theory developed here provides tools for the study of the structure of the centraliser lattice of partially commutative groups.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS

Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties of $Gamma(R)$ are studied. We investigate connectivity and the girth of $Gamma(R)$, where $...

متن کامل

Vicious Circles in Orthogonal Term Rewriting Systems

In this paper we first study the difference between Weak Normalization (WN) and Strong Normalization (SN), in the framework of first order orthogonal rewriting systems. With the help of the Erasure Lemma we establish a Pumping Lemma, yielding information about exceptional terms, defined as terms that are WN but not SN. A corollary is that if an orthogonal TRS is WN, there are no cyclic reductio...

متن کامل

ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS

Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.

متن کامل

General Cyclic Orthogonal Double Covers of Finite Regular Circulant Graphs

An orthogonal double cover (ODC) of a graph H is a collection ( ) { } v G v V H : = ∈  of ( ) V H subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC  of H is cyclic (CODC) if the cyclic group of order ( ) V H is a subgroup of the automorphism group of  . In this paper, we introduce a general orthogonal la...

متن کامل

On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008