L(h, K)-coloring

	L(h, K)-coloring In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ..., a L(''h'', ''k'')-labelling, L(''h'', ''k'')-coloring or sometimes L(''p'', ''q'')-coloring is a (proper) vertex coloring in which every pair of adjacent vertices has color numbers that differ by at least ''h'', and any nodes connected by a 2 length path have their colors differ by at least ''k''. The parameters, ''h'' and ''k'' are understood to be non-negative integers. The problem originated from a channel assignment problem in radio networks. The span of an L(''h'', ''k'')-labelling, ρh,k(G) is the difference between the largest and the smallest assigned frequency. The goal of the L(''h'', ''k'')-labelling problem is usually to find a labelling with minimum span. For a given graph, the minimum span over all poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Graph Theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''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 of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Graph Coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as-is. This is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	L(2,1)-coloring L(2, 1)-coloring is a particular case of L(h, k)-coloring In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') .... In an L(2, 1)-coloring of a graph, G, the vertices of G are assigned color numbers in such a way that adjacent vertices get labels that differ by at least two, and the vertices that are at a distance of two from each other get labels that differ by at least one. An L(2,1)-coloring is a proper coloring, since adjacent vertices are assigned distinct colors. References Graph coloring {{Combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]