On binary operation graphs

Manal Naji Al-Harere; Ahmed Abed Ali Omran

doi:10.5269/bspm.v38i7.44282

Manal Naji Al-Harere University of Technology http://orcid.org/0000-0003-1125-4439
Ahmed Abed Ali Omran University of Babylon

DOI: https://doi.org/10.5269/bspm.v38i7.44282

Abstract

A graph labeling is an assignment of integers to the vertices, edges, or to both, and it is subject to certain conditions. In this paper, a new concept of graph labeling called binary operation labeling is introduced. The graph is said to be a binary operation graph if admits a binary operation labeling. Some results for this new type of labeling are contributed.

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Author Biographies

Manal Naji Al-Harere, University of Technology

Department of Applied Sciences

Ahmed Abed Ali Omran, University of Babylon

College of Education for Pure Science, Department of Mathematics

References

B. D. Acharya, S. Arumugarn, and A. Rosa, Labeling of Discrete Structures and Applications, Narosa Publishing House, New Delhi, (2008).

M.N. Al-Harere, A. A. Omran, Binary operation graphs, AIP conference proceeding vol.2086, Maltepe University, Istanbul, Turkey,030008, 31 July - 6 August (2018). https://doi.org/10.1063/1.5095093

I. Arkut, R. Arkut, N. Ghani, Graceful label numbering in optical MPLS networks, In: Proc. SPIE, 4233 (2000) 1-8 OptiComm 2000: Optical Networking and Communications. Imrich Chlamtac: Ed (2000).

https://doi.org/10.1117/12.401809

I. C. Arkut, R. C. Arkut, and A. Basak, Topology constrained label switching for multicast routing, http://www.academia.edu/4370947/

A. Basak,MPLS multicasting using caterpillars and a graceful labelling scheme, IEEE Conference Publications, Information Visualisation, 2004. IV (2004), Proceedings. Eighth International Conference on, 382-387. https://doi.org/10.1109/iv.2004.1320172

J. C. Bermond,Graceful graphs, radio antennae and French windmills, Graph Theory and Combinatorics, Pitman, London 18-37, (1979).

G. S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N.Y. Acad. Sci., 326, 32-51, (1979).

https://doi.org/10.1111/j.1749-6632.1979.tb17766.x

G. S. Bloom and S. W. Golomb, Applications of numbered undirected graphs, Proc. IEEE, 65, 562-570, (1977).

https://doi.org/10.1109/PROC.1977.10517

G. S. Bloom and S. W. Golomb, Numbered complete graphs, unusual rulers, and assorted applications, in Theory and Applications of Graphs, Lecture Notes in Math., 642, Springer-Verlag, New York 53-65, (1978).

https://doi.org/10.1007/BFb0070364

J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, Twentieth edition, December 22,(2017).

J. A. Gallian,A survey: recent results, conjectures and open problems on labeling graphs,J. Graph Theory, 13, 491-504,(1989).

https://doi.org/10.1002/jgt.3190130410

J. A. Gallian, A guide to the graph labeling zoo, Discrete Appl. Math., 49, 213-229, (1994).

https://doi.org/10.1016/0166-218X(94)90210-0

R. L. Graham and N. J. A. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Methods, 1, 382-404, (1980).

https://doi.org/10.1137/0601045

F. Harary,Graph Theory, Addison-Wesely, Reading , Massachusetts ,(1969).

https://doi.org/10.21236/AD0705364

K. M. Koh, D. G. Rogers, and T. Tan, A graceful arboretum: a survey of graceful trees, in Proceedings of Franco-Southeast Asian Conference, Singapore, May 2, 278-287,(1979).

A. Meissner and K. Zwierzynski, Vertex-magic total labeling of a graph by distributed constraint solving in the Mozart System, in Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, 3911 Springer Berlin/Heidelberg, (2006).

https://doi.org/10.1007/11752578_115

J.F. Puget,Breaking symmetries in all different problems, in Proceedings of SymCon04, the 4th International Workshop on Symmetry in Constraints, (2004).

A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris 349-355, (1967).

M. A. Seoud and M. N. Al-Harere, Some non combination graphs, Applied Math. Sciences, 6, no. 131, 6515-6520, (2012).

M. A. Seoud and M. N. Al-Harere, Some notes on combination graphs, Ars Combin. , 129, 95-106, (2016).

M. A. Seoud and M. N. Al-Harere, Further results on square sum graphs, Nat. Acad. Sci. Lett., 37 (2014), no. 5, 473-475.

https://doi.org/10.1007/s40009-014-0264-1

B. M. Smith and J.-F. Puget,Constraint models for graceful graphs, Constraints 15, 64-92, (2010).

https://doi.org/10.1007/s10601-009-9071-6

M. Sutton,Sumable Graphs Labellings and Their Applications, Ph. D. Thesis, Dept. Computer Science, The University of Newcastle, (2001).

H. Wang, B. Yao, and M. Yao,Generalized edge-magic total labellings of models from researching networks, Inform. Sci., 279, 460-467, (2014).

https://doi.org/10.1016/j.ins.2014.03.132