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.

A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

In this paper, we define irregular interval-valued fuzzy graphs and their various classifications. Size of regular interval-valued fuzzy graphs is derived. The relation between highly and neighbourly irregular interval-valued fuzzy graphs are established. Some basic theorems related to the stated graphs have also been presented.

In this paper, we define irregular bipolar fuzzy graphs and its various classifications. Size of regular bipolar fuzzy graphs is derived. The relation between highly and neighbourly irregular bipolar fuzzy graphs are established. Some basic theorems related to the stated graphs have also been presented.

A graph is said to be a neighbourly irregular graph (or simply an NI graph) if every pair of its adjacent vertices have distinct degrees. Let G be a simple graph of order n. Let NI(G) denote the set of all NI graphs in which G is an induced subgraph. The neighbourly regular strength of G is denoted by NRS(G) and is defined as the minimum positive integer k for which there is an NI graph in NI(G...

We begin by associating to any sequence of vertices in a simple graph X, here always assumed connected, a partially ordered set called a heap. This terminology was introduced by Viennot ([11]) and used extensively by Stembridge in the context of fully commutative elements of Coxeter groups (see [8]), but our context is more general and graph-theoretic. The heap of a sequence of vertices is that...

In this paper we show that graphs of “neighbourly” cubical complexes – cubical complexes in which every pair of vertices spans a (unique) cube – have good expansion properties, using a technique based on multicommodity flows. By showing that graphs of stable set polytopes are graphs of neighbourly cubical complexes we give a new proof that graphs of stable set polytopes have edge expansion 1.