Fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees

AbstractA bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path joining every pair of vertices that are in different parts of the graph. It is well known that Cay(Sn,B) is Hamiltonian laceable, where Sn is the symmetric group on {1,2,…,n} and B is a generating set consisting of transpositions of Sn. In this paper, we show that for any F⊆E(Cay(Sn,B)), if |F|≤n−3 and n≥4, then there exists a Hamiltonian path in Cay(Sn,B)−F joining every pair of vertices that are in different parts of the graph. The result is optimal with respect to the number of edge faults

ONE BY ONE EMBEDDING THE CROSSED HYPERCUBE INTO PANCAKE GRAPH

Let G and H be two simple undirected graphs. An embedding of the graph G into the graph H is an injective mapping f from vertices of G to the vertices of H. The dilation of embedding is the maximum distance between f(u), f(v) taken over edges (u, v) of G. The Pancake graph is one as viable interconnection scheme for parallel computers, which has been examined by a number of researchers. The Pancake was proposed as alternatives to the hypercube for interconnecting processors in parallel computer. Some good attractive properties of this interconnection network include: vertex symmetry, small degree, a sub-logarithmic diameter, extendability, and high connectivity (robustness), easy routing and regularity of topology, fault tolerance, extensibility and embeddability of others topologies. In this paper, we give a construction of one by one embedding of dilation 5 of crossed hypercube into Pancake graph

Sets as graphs

The aim of this thesis is a mutual transfer of computational and structural results and techniques between sets and graphs. We study combinatorial enumeration of sets, canonical encodings, random generation, digraph immersions. We also investigate the underlying structure of sets in algorithmic terms, or in connection with hereditary graphs classes. Finally, we employ a set-based proof-checker to verify two classical results on claw-free graph

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008