Definition
Given a graph G, we denote the set of edges by E(G) and the 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 u 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 the vertex u is given by
where V(u) is the label for the vertex and E(e) is the assigned value of an edge incident to u.
The problem is to find a labeling for the edges such that all the labels from 1 to q are used once and the induced labels on the vertices run from 0 to p − 1. In other words, the resulting set for labels of the edges should be and for the vertices.
A graph G is said to be edge-graceful if it admits an edge-graceful labeling.
Read more about this topic: Edge-graceful Labeling
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)