Hamiltonian Cycles in Directed Toeplitz Graphs

نویسندگان

  • Shabnam Malik
  • Ahmad Mahmood Qureshi
چکیده

Hamiltonian Cycles in Directed Toeplitz Graphs Dr Shabnam Malik Faculty of Mathematics, Forman Christian College University, Lahore Pakistan An (n × n) matrix A = (aij) is called a Toeplitz matrix if it has constant values along all diagonals parallel to the main diagonal. A directed Toeplitz graph is a digraph with Toeplitz adjacency matrix. In this talk I will discuss conditions for the existence of hamiltonian cycles in directed Toeplitz graphs.

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

Hamiltonian properties of Toeplitz graphs

Condit ions are given for the existence of hamiltonian paths and cycles in the so-called Toeplitz graphs, i.e. simple graphs with a symmetric Toeplitz adjacency matrix.

متن کامل

Upper Bounds for the Number of Hamiltonian Cycles

Abstract. An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the famous Minc’s bound and the Brégman’s bound. A transformation on graphs is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be done by counting the number of Hamiltonian cycles of its corresponding symmetric dire...

متن کامل

When the Cartesian Product of Directed Cycles is

The Cartesian product of two hamiltonian graphs is always hamiltonian. For directed graphs, the analogous statement is false. We show that the Cartesian product C,,, x C,, of directed cycles is hamiltonian if and only if the greatest common divisor (g.c.d.) d of n, and n, is a t least two and there exist positive integers d,, d, so that d, + d, = d and g.c.d. (n,, d,) = g.c.d. (n,, d,) = 1. We ...

متن کامل

Improved Sufficient Conditions for the Existence of Anti-Directed Hamiltonian Cycles in Digraphs

Let D be a directed graph of order n. An anti-directed (hamiltonian) cycleH inD is a (hamiltonian) cycle in the graph underlyingD such that no pair of consecutive arcs in H form a directed path in D. In this paper we give sufficient conditions for the existence of anti-directed hamiltonian cycles. Specifically, we prove that a directed graph D of even order n with minimum indegree and outdegree...

متن کامل

On a Simple Randomized Algorithm for Finding Long Cycles in Sparse Graphs

We analyze the performance of a simple randomized algorithm for finding long cycles and 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O(n) expected time. The analysis of our algorithm is based on random walks on a line and interestingly resembles the analys...

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:
  • Ars Comb.

دوره 109  شماره 

صفحات  -

تاریخ انتشار 2013