The point-distinguishing chromatic index of a graph represents the minimum number of colours in its edge colouring such that each vertex is distinguished by the set of colours of edges incident with it. Asymptotic information on jumps of the point-distinguishing chromatic index of Kn,n is found.

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.

Definition 1. A directed hypergraph of uniformity k is a pair (V,E) with E ⊆ V k. The chromatic number of a directed hypergraph is the chromatic number of the associated undirected hypergraph, that is, the least number χ such that there exists a function f : V → [χ] such that for each edge e ∈ E, not all of f(e1), ..., f(ek) are equal. We’ll assume that no edge of E has any two coordinates equa...

Hajj os theorem states that every graph with chromatic number at least k can be obtained from the complete graph K k by a sequence of simple operations such that every intermediate graph also has chromatic number at least k. Here, Hajj os theorem is extended in three slightly diierent ways to colorings and circular colorings of edge-weighted graphs. These extensions shed some new light on the H...

The strong chromatic index of graphs Mohammad Mahdian Master of Science Graduate Department of C o m p t e r Science University of Toronto 2000 A strong edge-colouring of a graph G is an assignrnent of colours to the edges of G such that every colour class is an induced matching. The minimum number of colours in such a colouring is called the strong chromatic index of G. In 1985, Erdos and Nese...

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...