A balanced bipartite graph G is said to be 2p-Hamilton-biconnected if for any balanced subset W of size 2p of V (G), the subgraph induced by V (G)\W is Hamilton-biconnected. In this paper, we prove that “ Let p ≥ 0 and G be a balanced bipartite graph of order 2n with minimum degree δ(G) ≥ k, where n ≥ 2k − p + 2 and k ≥ p. If the number of edges e(G) > n(n − k + p− 1) + (k+2)(k−p+1), then G is ...

Let G = (X, Y ; E) be a balanced 2-connected bipartite graph and S ⊂ V(G). We will say that S is cyclable in G if all vertices of S belong to a common cycle in G. We give sufficient degree conditions in a balanced bipartite graph G and a subset S ⊂ V(G) for the cyclability of the set S.

Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. The matching preclusion number of a graph G is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching, and the conditional matching preclusion number of G is the minimum number of edges whose deletion leaves the resultin...

In this paper we prove that any distance-balanced graph G with ∆(G) ≥ |V (G)| − 3 is regular. Also we define notion of distancebalanced closure of a graph and we find distance-balanced closures of trees T with ∆(T ) ≥ |V (T )| − 3.

In this paper we present a model for the study of the total balancedness of packing and covering games, concerning some aspects of graph theory. We give an alternative proof of van Velzen’s characterization of totally balanced covering games. We introduce new types of graph perfection, which allows us to give another approach to the open problem of characterizing totally balanced packing games.

Network science makes heavy use of simulation models and calculations based upon graph-oriented data structures that are intrinsically highly irregular in nature. The key to efficient use of data-parallel and multi-core parallelism on graphical processing units (GPUs) and CPUs is often to optimise the data layout and to exploit distributed memory locality with processing elements. We describe w...

Computation of homology generators using an irregular graph pyramid can significantly increase performance compared to the classical methods. First results in 2D exist and show the advantages of the method. The generators are computed in upper levels of pyramid where it is known that the graphs contains a number of self loops and multiple edges product of the contraction processes. Using a stra...

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...

Biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability in which strong excitatory synaptic inputs are canceled by strong inhibitory inputs on average, and irregular spiking activity is driven by fluctuating synaptic currents. Most previous studies of balanced networks assume a homogeneous or distance-dependent conn...

In this paper we study a 2-color analog of the cycle cone of a graph. Suppose the edges of a graph are colored red and blue. A nonnegative real vector on the edges is said to be balanced if the red sum equals the blue sum at every vertex. A balanced subgraph is a subgraph whose characteristic vector is balanced (i.e., red degree equals blue degree at every vertex). By a sum (respectively, fract...