A Study on Co – odd (even) Sum Degree Edge Domination Number in Graphs

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V Mohana Selvi
P Usha
D Ilakkiya


 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domination value is defined.  Further, the exact values of the above said parameters are found for some standard classes of graphs.  The bounds of the co-odd (even) sum degree edge domination number are obtained in terms of basic graph terminologies.  The co-odd (even) sum degree edge dominating sets are characterized.  The relationships with other edge domination parameters are also studied.


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Selvi VM, Usha P, Ilakkiya D. A Study on Co – odd (even) Sum Degree Edge Domination Number in Graphs. Baghdad Sci.J [Internet]. 2023 Mar. 1 [cited 2023 Mar. 21];20(1(SI):0359. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8424


Shalaan MM, Omran AA. Co-even Domination in Graphs. Int J Control Autom. 2020; 13(3): 330-334. https://www.researchgate.net/profile/Ahmed-Omran-17/publication/343376769_Co-Even_Domination_In_Graphs/links/5f25eec8a6fdcccc43a24129/Co-Even-Domination-In-Graphs.pdf

Jeba JJ, Vinodhini NK, Subiksha KSD. Prime Labeling of Certain Graphs. Bull Pure Appl Sci Sec .E - math. stat. 2021; 40(2): 167- 171. https://doi.org/10.5958/2320-3226.2021.00019.9

Shalaan MM, Omran AA. Co-Even Domination Number in Some Graphs. IOP Conf Ser.: Mater Sci Eng. 2020; 928: 1-7. https://iopscience.iop.org/article/10.1088/1757-899X/928/4/042015

Harary F. Graph Theory. USA: Addison – Wesley; 1972.

Caro Y, Klostermeyer W. The Odd Domination Number of a Graph. J Comb Math Comb Comput. 2003; 44(3): 65-84. https://doi.org/10.7151/dmgt.1137

Kinsley AA, Karthika K. Odd Geo-Domination Number of a Graph. STD. 2020; 9(12): 442-447. https://drive.google.com/file/d/1pmZ56OjVyt_EPE9tVjimXf9_DqpjsnvG/view

Kumar UVC, Murali R, Girisha A. Edge Domination in Some Brick Product Graphs. TWMS J App Eng Math. 2020; 10(1): 173-180. https://jaem.isikun.edu.tr/web/images/articles/vol.10.no.1/17.pdf

Al-Harere MN, Mitlif RJ, Sadiq FA. Variant Domination Types for a Complete h-ary Tree. Baghdad Sci. J. 2021; 18(1): 2078-8665. https://doi.org/10.21123/bsj.2021.18.1(Suppl.).0797

Omran AA, Ibrahim TA. Whole Domination in Graphs. TWMS J. App. and Eng. Math. 2022; 12(4): 1506-1511. https://jaem.isikun.edu.tr/web/index.php/archive/117-vol12no4/932

Gallian JA. A Dynamic Survey of Graph Labeling. Electron. J. Comb. 2022; 1-623. https://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/DS6/pdf

Al-Harere MN, Bakhash PAK. Tadpole Domination in Graphs. Baghdad Sci. J. 2018; 15(4): 466-471. https://doi.org/10.21123/bsj.2018.15.4.0466