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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 ...
This is a list of graph theory topics, ... Graph two-coloring; Harmonious coloring; ... Graph labeling. Graceful labeling; Graph partition;
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 ...
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Graph labeling#Harmonious labelings
A friendly labeling of an n-vertex undirected graph G = (V,E) is defined to be an assignment of the values 0 and 1 to the vertices of G with the property that the number of vertices labeled 0 is as close as possible to the number of vertices labeled 1: they should either be equal (for graphs with an even number of vertices) or differ by one ...
Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color; thus χ H (G) ≤ | V(G) |. There trivially exist graphs G with χ H (G) > χ(G) (where χ is the chromatic number); one example is any path of length > 2, which can be 2-colored but has no harmonious coloring with 2 colors. Some properties of χ H ...
A logarithmic chart allows only positive values to be plotted. A square root scale chart cannot show negative values. x: the x-values as a comma-separated list, for dates and time see remark in xType and yType; y or y1, y2, …: the y-values for one or several data series, respectively. For pie charts y2 denotes the radius of the corresponding ...
The vertex set of an n-vertex graph may be identified with the integers from 1 to n, and using such an identification a canonical form of a graph may also be described as a permutation of its vertices. Canonical forms of a graph are also called canonical labelings, [4] and graph canonization is also sometimes known as graph canonicalization.