Journal of Applied and Industrial Mathematics

, Volume 2, Issue 3, pp 379–384

# Unicyclic nonintegral sum graphs

Article

## 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).
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).
4. 4.
S. C. Liaw, D. Kuo, and G. Chang, “Integral Sum Numbers of Graphs,” Ars Combinatoria 54, 259–268 (2000).
5. 5.
L. S. Melnikov and A. V. Pyatkin, “Regular Integral Sum Graphs,” Discrete Math. 252(1–3), 237–245 (2002).
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).
8. 8.
J. Wu, J. Mao, and D. Li, “New Types of Integral Sum Graphs,” Discrete Math. 260(1–3), 163–176 (2003).
9. 9.
B. Xu, “On Integral Sum Graphs,” Discrete Math. 194(1–3), 285–294 (1999).