In practice, wireless networks has the property that the signal strength attenuates with respect to the distance from the base station, it could be better if the nodes at two hop away are considered for better quality of service. In this paper, we propose a procedure to identify delay preserving substructures for a given wireless ad-hoc network using a new graph operation G 2 – E (G) = G* (Edge...

A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2–factored snarks. In particular, we construct two new odd 2–factored snarks that disprove a conjecture by some of the authors. Moreover, w...

Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover Q and a stable set cover S s.t. every clique in Q intersects every stable set in S. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (K ̈orner [6]) and graph entropy (Czisz ́ar et al. [5]). Perfect graphs have been recently characterized a...

Let G be a simple graph and f : V (G) 7→ {1, 3, 5, ...} an odd integer valued function defined on V (G). A spanning subgraph F of G is called a (1, f)odd factor if dF (v) ∈ {1, 3, ..., f(v)} for all v ∈ V (G), where dF (v) is the degree of v in F . For an odd integer k, if f(v) = k for all v, then a (1, f)odd factor is called a [1, k]-odd factor. In this paper, the structure and properties of a...

The odd edge connectivity of a graph G, denoted by o(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and be a positive real number. We proved that there is a function fS( ) (depends on the surface S and lim !0 fS( )1⁄41) such that any graph G embedded in S with the odd-edge connectivity at least fS( ) admits a nowhere-zero circular (2þ )-flow. Another major r...

The even graceful labeling of a graph G with q edges means that there is an injection f : V(G) to { 0,1,1,1,2,...,2q+i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {1,3,5,...,2q-1}. A graph which admits an edge odd graceful labeling is called an edge-odd graceful graph. In this paper, the edge odd gracefulness of paths p1, p2, p3,..., ...

We consider the problem of computing Skolem functions for satisfied dependency quantified Boolean formulas (DQBFs). We show how Skolem functions can be obtained from an elimination-based DQBF solver and how to take preprocessing steps into account. The size of the Skolem functions is optimized by don’t-care minimization using Craig interpolants and rewriting techniques. Experiments with our DQB...

We consider the following question: can split graphs with odd maximum degree be edge-coloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case the graph has a quasi-universal vertex.

An even-cycle decomposition of a graph G is a partition of E(G) into cycles of even length. Evidently, every Eulerian bipartite graph has an even-cycle decomposition. Seymour (1981) proved that every 2-connected loopless Eulerian planar graph with an even number of edges also admits an even-cycle decomposition. Later, Zhang (1994) generalized this to graphs with no K5-minor. Our main theorem gi...