Search results
Results From The WOW.Com Content Network
A "harmonious labeling" on a graph G is an injection from the vertices of G to the group of integers modulo k, where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge (x, y) to be the sum of the labels of the two vertices x, y (mod k). A "harmonious graph ...
A graceful labeling. Vertex labels are in black, edge labels in red.. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m ...
A labeled graph is a graph whose vertices or edges have labels. The terms vertex-labeled or edge-labeled may be used to specify which objects of a graph have labels. Graph labeling refers to several different problems of assigning labels to graphs subject to certain constraints. See also graph coloring, in which the labels are interpreted as ...
Given a graph G, we denote the set of its edges by E(G) and that of its vertices by V(G). Let q be the cardinality of E(G) and p be that of V(G). Once a labeling of the edges is given, a vertex of the graph is labeled by the sum of the labels of the edges incident to it, modulo p. Or, in symbols, the induced labeling on a vertex is given by
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Graph labeling#Harmonious labelings
A vertex-signed graph, sometimes called a marked graph, is a graph whose vertices are given signs. A circle is called consistent (but this is unrelated to logical consistency) or harmonious if the product of its vertex signs is positive, and inconsistent or inharmonious if the product is negative. There is no simple characterization of ...
In graph theory, a harmonious coloring is a (proper) vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. It is the opposite of the complete coloring , which instead requires every color pairing to occur at least once.
[1] [2] The 7-page book graph of this type provides an example of a graph with no harmonious labeling. [2] A second type, which might be called a triangular book, is the complete tripartite graph K 1,1,p. It is a graph consisting of triangles sharing a common edge. [3] A book of this type is a split graph.