Jixiang Meng

On strongly Z 2s+1 -connected graphs

Abstract An orientation of a graph G is a mod ( 2 s + 1 ) -orientation if under this orientation, the net out-degree at every vertex is congruent to zero mod ( 2 s + 1 ) . If for any function b : V ( G ) → Z 2 s + 1 satisfying ∑ v ∈ V ( G ) b ( v ) ≡ 0 ( mod 2 s + 1 ) , G always has an orientation D such that the net out-degree at every vertex v is congruent to b ( v ) mod ( 2 s + 1 ) , then G is strongly Z 2 s + 1 -connected. In this paper, we prove that a connected graph has a mod ( 2 s + 1 ) -orientation if and only if it is a contraction of a ( 2 s + 1 ) -regular bipartite graph. We also proved that every ( 4 s − 1 ) -edge-connected series–parallel graph is strongly Z 2 s + 1 -connected, and every simple 4 p -connected chordal graph is strongly Z 2 s + 1 -connected.

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

Abstract A 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 C a y ( S n , B ) is Hamiltonian laceable, where S n is the symmetric group on { 1 , 2 , … , n } and B is a generating set consisting of transpositions of S n . In this paper, we show that for any F ⊆ E ( C a y ( S n , B ) ) , if | F | ≤ n − 3 and n ≥ 4 , then there exists a Hamiltonian path in C a y ( S n , 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.

Note: Super edge-connectivity of mixed Cayley graph

A graph X is max-@l if @l(X)=@d(X). A graph X is super-@l if X is max-@l and every minimum edge-cut set of X isolates one vertex. In this paper, we proved that for all but a few exceptions, the mixed Cayley graph which is defined as a new kind of semi-regular graph is max-@l and super-@l.

Hamiltonian jump graphs

Let G be a nonempty graph. The jump graph J(G) of G is the graph whose vertices are edges of G, and where two vertices of J(G) are adjacent if and only if they are not adjacent in G. Equivalently, the jump graph J(G) of G is the complement of line graph L(G) of G. In this paper, we characterize hamiltonian jump graphs and settle two conjectures posed by Chartrand et al. on jump graphs.

Reliability analysis of bijective connection networks in terms of the extra edge-connectivity

Reliability evaluation of interconnection network is of significant importance to the design and maintenance of multiprocessor systems. The extra edge-connectivity (also called restricted edge-connectivity) is an important parameter for the reliability evaluation of interconnection network. In this paper, we find a method to study the h-extra edge-connectivity of an n-dimensional bijective connection network (in brief, BC network, also called hypercube-like network). As an application, we determine h-extra edge-connectivity of an n-dimensional BC network is a constant 2n-1 for 2n-1+2f3⩽h≤2n-1,n⩾4, where f=0 when n is even, and f=1 when n is odd. We also show that the lower bound of h is sharp. This paper also obtains the exact value of h-extra edge-connectivity of an n-dimensional BC network for 1⩽h⩽2⌊n2⌋+1,n⩾4. Besides, since the BC network includes several well-known network models, such as, hypercubes, twisted cubes, crossed cubes, Mobius cubes, locally twisted cubes, generalized twisted cubes and Mcubes, so the previous results on the h-extra edge-connectivity of these networks are our corollaries.

Gaussian integral circulant digraphs

The spectrum of a digraph in general contains real and complex eigenvalues. A digraph is called a Gaussian integral digraph if it has a Gaussian integral spectrum that is all eigenvalues are Gaussian integers. In this paper, we consider Gaussian integral digraphs among circulant digraphs.

A classification of 2-arc-transitive circulant digraphs

A class cation of 2-arc-transitive circulant digraphs is given. c

On the isomorphism problem of Cayley graphs of Abelian groups

Abstract A group G is called a DCIM-group if any minimal generating subset of G is a CI-subset. Here, the Abelian DCIM-groups are characterized.

Matching preclusion for n-dimensional torus networks

Abstract The matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings. Wang et al. [13] proved that a class of n -dimensional tours networks with even order are super matched. Later, Cheng et al. [8] further showed that all n -dimensional tours networks with even order are super matched. In this paper, we prove that all n -dimensional torus networks with odd order are super matched if n ≥ 3 . Two-dimensional torus networks with odd order is maximally matched except for C 3 □ C 3 . Our results are complementary to those of Wang et al. [13] and Cheng et al. [8] .

Semi-hyper-connected edge transitive graphs

A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characterize semi-hyper-connected edge transitive graphs.