SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES
نویسندگان
چکیده مقاله:
In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ for all $m,ngeq2$
منابع مشابه
solvability of free products, cayley graphs and complexes
in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...
متن کاملCayley graphs - Cayley nets
It is, however, not clear how to choose the generators to produce special graphs. We know many topologies and their generators, but many more may be constructed in the future, having better properties (in terms of diameter, nodal degree and connectivity) than for instance the hypercube. I will present several graphs which connect rings using the generator g 1 and some additional generators.
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کاملProduct of normal edge-transitive Cayley graphs
For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
متن کاملDomination and Signed Domination Number of Cayley Graphs
In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.
متن کاملComputing Wiener and hyper–Wiener indices of unitary Cayley graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 1 شماره 1
صفحات 45- 52
تاریخ انتشار 2013-09-15
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023