Generalized Matching Preclusion in Bipartite Graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes

Generalized Matching Preclusion in Bipartite Graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Let G be a graph. Then T subset of V(G) is called an R(k)-vertex-cut if G - T is disconnected and each vertex in V(G) - T has at least k neighbors in G - T. The size of a smallest R(k)-vertex-cut is the R(k)-vertex-connectivity of G and is denoted by kappa(k)(G). In this paper, we determine the numbers kappa(1) and kappa(2) for Cayley graphs generated by 2-trees, including the popular alternating group graphs. (C) 2011 Elsevier Inc. All rights reserved

On the edge-connectivity of graphs with two orbits of the same size

CSC; NSFC [10831001, 10971255]; Chinese Ministry of Education [208161]; Program for New Century Excellent Talents in University; Fundamental Research Funds for the Central Universities, China [2010121076]; National Natural Science Foundation of China [5 1It is well known that the edge-connectivity of a simple, connected, vertex-transitive graph attains its regular degree. It is then natural to consider the relationship between the graph's edge-connectivity and the number of orbits of its automorphism group. In this paper, we discuss the edge connectedness of graphs with two orbits of the same size, and characterize when these double-orbit graphs are maximally edge connected and superedge-connected. We also obtain a sufficient condition for some double-orbit graphs to be lambda'-optimal. Furthermore, by applying our results we obtain some results on vertex/edge-transitive bipartite graphs, mixed Cayley graphs and half vertex-transitive graphs. (C) 2011 Elsevier B.V. All rights reserved

Synthesis and chiroptical properties of (naphthyl)ethylidene ketals of carbohydrates in solution and solid state

1,3-Dioxolane- and dioxane-type (1- and 2-naphthyl)ethylidene ketals of p-methoxyphenyl α-l-rhamnopyranoside and β-d-glucopyranoside were prepared and their stereochemistry studied by solution and solid-state circular dichroism, X-ray diffraction, and coupled-oscillator CD calculations on the solid-state and MMFF-calculated geometries. Intermolecular exciton-coupled interactions between the nearby aromatic chromophores in the solid state and different conformers in solution and solid state could be identified as the main reason for the difference between solution and solid-state CDs