Journal of Applied and Industrial Mathematics

, Volume 2, Issue 3, pp 379–384 | Cite as

Unicyclic nonintegral sum graphs

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Abstract

A graph G = (V,E) is an integral sum graph if there exists a labeling S(G) ⊂ Z such that V = S(G) and every two distinct vertices u, υV are adjacent if and only if u + υV. A connected graph G = (V,E) is called unicyclic if |V| = |E|. In this paper two infinite series are constructed of unicyclic graphs that are not integral sum graphs.

Keywords

Industrial Mathematic Connected Graph Discrete Math Edge Incident Distinct Vertex 

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References

  1. 1.
    Z. Chen, “Integral Sum Graphs From Identification,” Discrete Math. 181(1–3), 77–90 (1998).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. A. Gallian, “A Dynamic Survey of Graph Labeling,” http://www.combinatorics.org/Surveys/ds6.pdf.
  3. 3.
    F. Harary, “Sum Graphs Over All Integers,” Discrete Math. 124(1–3), 99–105 (1994).MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. C. Liaw, D. Kuo, and G. Chang, “Integral Sum Numbers of Graphs,” Ars Combinatoria 54, 259–268 (2000).MATHMathSciNetGoogle Scholar
  5. 5.
    L. S. Melnikov and A. V. Pyatkin, “Regular Integral Sum Graphs,” Discrete Math. 252(1–3), 237–245 (2002).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    T. Nicholas and S. Somasundaram, “More Results on Integral Sum Graphs,” in Proceedings of National Conference on Graph Theory and Its Applications (Chennai, 2001).Google Scholar
  7. 7.
    A. Sharary, “Integral Sum Graphs From Complete Graphs, Cycles, and Wheels,” Arab Gulf J. Sci. Res. 14(1), 1–14 (1996).MATHMathSciNetGoogle Scholar
  8. 8.
    J. Wu, J. Mao, and D. Li, “New Types of Integral Sum Graphs,” Discrete Math. 260(1–3), 163–176 (2003).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    B. Xu, “On Integral Sum Graphs,” Discrete Math. 194(1–3), 285–294 (1999).MATHMathSciNetGoogle Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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