δ and prime-labelling of a tree from caterpillars

Sethukkarasi, A.; Vidyanandini, S.; Nayak, Soumya Ranjan

doi:10.47974/JDMSC-2090

Open Access Research Article

δ and prime-labelling of a tree from caterpillars

A. Sethukkarasisa0421@srmist.edu.inDepartment of MathematicsSRM Institute of Science and TechnologyCollege of Engineering and TechnologyKattankulathur, Tamil Nadu, 603202, IndiaView full profile → , ^*S. VidyanandiniCorresponding authorvidyanas@srmist.edu.inDepartment of MathematicsSRM Institute of Science and TechnologyCollege of Engineering and TechnologyKattankulathur, Tamil Nadu, 603202, IndiaView full profile → , Soumya Ranjan Nayaknayak.soumya17@gmail.comSchool of Computer EngineeringKalinga Institute of Industrial Technology (Deemed to be University)Bhubaneswar, Odisha, 751024, IndiaView full profile →

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pp. 2179–2190Vol. 27Issue 7October 2024DOI: 10.47974/JDMSC-2090 Crossmark XML

Received:: 06 Mar 2024
Published Online:: 15 Oct 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2090
Pages:: 2179–2190

Abstract

This paper explores δ-labelling and prime labelling for trees derived from caterpillar structures. In δ-labelling, vertex labels induce injective edge labels, while prime labelling ensures adjacent vertices have a greatest common divisor of one. An algorithm for efficiently labelling caterpillar trees using both methods is introduced. These labelling techniques have practical applications in network security and cryptography, providing new strategies to strengthen the security and robustness of communication networks and cryptographic systems.

Keywords

δ - Labelling Prime labelling Tree and caterpillars

Subject Classifications

Primary 05C78Secondary 05C69

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