Different types of odd harmonious labeling of super subdivision of various graphs

Deen, Mohamed R. Zeen El; Elmahdy, Ghada M.

doi:10.47974/JDMSC-1945

Open Access Research Article

Different types of odd harmonious labeling of super subdivision of various graphs

^*Mohamed R. Zeen El DeenCorresponding authormohamed.zeeneldeen@sci.suezuni.edu.egDepartment of Mathematics and Computer Science Faculty of Science Suez UniversitySuez, 43221, EgyptView full profile → , Ghada M. Elmahdyghada.elmahdy91@gmail.comDepartment of Basic Science Canal High Institute of Engineering and TechnologySuez, 43111, EgyptView full profile →

* Corresponding author · click or hover a name for details

pp. 2373–2407Vol. 27Issue 8December 2024DOI: 10.47974/JDMSC-1945 Crossmark XML

Received:: 12 Sep 2023
Published Online:: 18 Dec 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1945
Pages:: 2373–2407

Abstract

If the vertices of a graph Γ(α, β), with α = |V(Γ)| and β = |E(Γ)|, can be labelled with unequal integers within the set [0, 2β – 1], so that the edges labels generated by the sum of the labels of the end vertices modulo 2β are distinct odd numbers from the set [1, 2β – 1]. Then, we regard the graph Γ(V, E) to be a semi-odd harmonic graph. An odd harmonious graph satisfies the additional condition that modular asthmatic is not done. A strong odd harmonious graph is defined as an odd harmonious graph whose vertices can be labelled with unequal integers from the set [0, β]. In this study, we introduce semi-odd harmonious labeling, which is an extension of odd harmonious labeling. We establish the existence of semi-odd harmonious labeling for the super subdivision of the following graphs: Y–tree, the graph Tg, g–2, the graph Pg ○K1, as well as the twig and crown graph. We demonstrate odd harmonious labeling for the super subdivision of the subsequent graphs: cycle, dragon graph Pm(Cg), wheel graph, friendship graph Frg, dumbbell graph Dbm,g, fan graph and the helm graph. The presence of strong odd harmonious labeling for the super subdivision is shown in the final section.

Keywords

Semi-odd harmonious labeling Strongly odd harmonious Super subdivision graphs

Subject Classifications

05C7805C90

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