Let G = (V, E) bea simple, finite and undirected graphs. A sum labeling is a one to one mapping L from a set of vertices of G to a finite set of positive integers S such that if u and v aire vertices of G then uv is an edge in G if and only if there is a vertex w in G and L(w) = L(u) + L(v). A graph G that has a sum labeling is called sum graph. The minimal isolated vertex that needed to make G a sum labeling is called sum number of G, notated as σ(G). The sum number of a sum graph G always greater or equal to δ(G), a minimum degree of G. An optimum sum graph is a sum graph that has σ(G) = δ(G). In this paper, we discuss sum numbers of finite union of some family of optimum sum graphs, such as cycles and friendship graphs.
|Number of pages||6|
|Journal||Journal of Combinatorial Mathematics and Combinatorial Computing|
|Publication status||Published - May 2008|
- Complete graphs and friendship graphs
- Optimal sum labeling