A connected graph is called neighbourly irregular (NI) if it contains no edge between the vertices of the same degree. In this paper we determine the upper bound for chromatic number of a neighbourly irregular graph. We also prove some results on neighbourly irregular graphs and its chromatic number.

Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes the topological category (local max, min, slope, saddle) of the gray level landscape around the center region. Given a 2D grayscale image I, our goal is to obtain a simplified image which can be seen as “minimal” representation in terms of topological characterization of I....

An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented hypergraphs. Oriented hypergraphs are further decomposed into three families – balanced, balanceable, and unbalanceable – and we obtain a complete classificati...

Parallel programming/execution frameworks for many/multi-core platforms should support as many applications as possible. In general, work-stealing frameworks provide efficient load balancing even for irregular parallel applications. Unfortunately, naı̈ve parallel programs which traverse graph-based data structures (e.g., for constructing spanning trees) cause stack overflow or unacceptable load ...

uzzy graph theory is finding an increasing number of applications in modeling real time systems where the level of information inherent in the system varies with different levels of precision. In the applied field, the success of the use of fuzzy set theory depends on the choice of the membership function that we make. However, there are applications in which experts do not have precise knowled...

Let G be a connected graph with maximum degree ∆(G). The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. We say that G is maximally irregular if t(G) = ∆(G). The purpose of this note, apart from pointing out that every highly irregular graph is maximally irregular, is to establish upper bounds on the size of maximally irregular graphs and max...

By a game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a nonempty set of payo®s for each coalition of players. It is well-known that balancedness is a su±cient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. But any information on the internal organization of the c...