Interval Edge Coloring
In graph theory, interval edge coloring is a type of edge coloring in which edges are labeled by the integers in some Interval (mathematics), interval, every integer in the interval is used by at least one edge, and at each vertex the labels that appear on incident edges form a consecutive set of distinct numbers. History The concept of consecutive edge-coloring was introduced with the terminology 'interval edge coloring' by Asratian and Kamalian in 1987 in their paper "Interval colorings of edges of a multigraph". Since interval edge coloring of graphs was introduced mathematicians have been investigating the existence of interval edge colorable graphs as not all graphs allow interval edge coloring. A simple family of graphs that allows interval edge coloring is complete graph of even order and a counter example of family of graphs includes complete graphs of odd order. The smallest graph that does not allow interval colorability. There are even graphs discovered with 28 vertices a ...
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Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ...
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