Optimum sum labeling of finite union of sum graphs

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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.

Original languageEnglish
Pages (from-to)133-138
Number of pages6
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
Publication statusPublished - May 2008


  • Complete graphs and friendship graphs
  • Cycles
  • Optimal sum labeling


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