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Harmonious labeling. 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 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 ...
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. The harmonious chromatic number χH(G) of a graph G is the minimum number of colors ...
The 7-page book graph of this type provides an example of a graph with no harmonious labeling. 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. A book of this type is a split graph.
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Graph labeling#Harmonious labelings
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. 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 ...
Hazard pictograms are one of the key elements for the labelling of containers under the GHS, along with: [2] an identification of the product; a signal word – either Danger or Warning – where necessary. hazard statements, indicating the nature and degree of the risks posed by the product. precautionary statements, indicating how the product ...
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 ...