# Search results

The Journal of Supercomputing > 2018 > 74 > 6 > 2638-2655

Discussiones Mathematicae Graph Theory > 2015 > 35 > 2 > 271-281

Journal of Combinatorial Optimization > 2012 > 24 > 4 > 627-646

*n*and

*k*be positive integers with

*n*−

*k*≥2. The arrangement graph

*A*

_{ n,k }is recognized as an attractive interconnection networks. Let

**x**,

**y**, and

**z**be three different vertices of

*A*

_{ n,k }. Let

*l*be any integer with $d_{A_{n,k}}(\mathbf{x},\mathbf{y}) \le l \le \frac{n!}{(n-k)!}-1-d_{A_{n,k}}(\mathbf{y},\mathbf{z})$ . We shall prove the following existance properties of Hamiltonian path: (1) for...

Applied Mathematics and Computation > 2010 > 217 > 8 > 4017-4023

_{0},v

_{1},…,v

_{m}〉 is a sequence of adjacent vertices. Two paths with equal length P

_{1}=〈 u

_{1},u

_{2},…,u

_{m}〉 and P

_{2}=〈 v

_{1},v

_{2},…,v

_{m}〉 from a to b are independent if u

_{1}=v

_{1}=a, u

_{m}=v

_{m}=b, and u...

Information Sciences > 2010 > 180 > 19 > 3781-3793

_{G}(x,y)⩽l⩽∣V(G)∣−1, where d

_{G}(x,y) denotes the distance between vertices x and y in G, and V(G) denotes the vertex set of G. For insight into the concept of panconnectedness, we propose a more refined property, namely panpositionable panconnectedness...

Graphs and Combinatorics > 2010 > 26 > 2 > 225-242

*H*be a multigraph, possibly containing loops. An

*H*-subdivision is any simple graph obtained by replacing the edges of

*H*with paths of arbitrary length. Let

*H*be an arbitrary multigraph of order

*k*, size

*m*,

*n*

_{0}(

*H*) isolated vertices and

*n*

_{1}(

*H*) vertices of degree one. In Gould and Whalen (Graphs Comb. 23:165–182, 2007) it was shown that if

*G*is a simple graph of order

*n*containing an

*H*-subdivision...

Discrete Mathematics > 2009 > 309 > 10 > 3013-3022

Applied Mathematics and Computation > 2008 > 198 > 1 > 414-432

_{n,k}is a generalization of the star graph. It is more flexible in its size than the star graph. There are some results concerning hamiltonicity and pancyclicity of the arrangement graphs. In this paper, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two different vertices x and y of G and for any integer...

Theoretical Computer Science > 2008 > 390 > 1 > 70-80

Theoretical Computer Science > 2007 > 377 > 1-3 > 170-180

Information Processing Letters > 2007 > 101 > 6 > 227-232

Parallel Computing > 2007 > 33 > 1 > 36-42

_{n}, the augmented cube AQ

_{n}, proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks, 40(2) (2002), 71–84], not only retains some of the favorable properties of Q

_{n}but also possesses some embedding properties that Q

_{n}does not. For example, AQ

_{n}contains cycles of all lengths from 3 to 2 ...