Graceful labeling of paths, cycles and caterpillars via inverse transformation

Pattanaik, Bijayani; Behera, Amiya Kumar; Bohidar, Chapala; Bhatta, Debi Prasad; Sethi, Bijaya Kumar

doi:10.47974/JDMSC-2603

Open Access Research Article

Graceful labeling of paths, cycles and caterpillars via inverse transformation

Bijayani Pattanaikbijayanipattanaik27@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , ^*Amiya Kumar BeheraCorresponding authoramiyabehera@soa.ac.inDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , Chapala Bohidarchapalabohidar@soa.ac.inDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Department of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University) Bhubaneswar, Odisha, 751030, IndiaView full profile → , Debi Prasad Bhattadebiprasadbhatta@soa.ac.inDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Department of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , Bijaya Kumar Sethisbijayakumar@gmail.comDepartment of Computer Science and Engineering (Data Science) Vardhaman College of Engineering (Autonomous)Hyderabad, Telangana, 501218, IndiaView full profile →

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pp. 1441–1459Vol. 29Issue 3March 2026DOI: 10.47974/JDMSC-2603 Crossmark XML

Received:: 01 Apr 2025
Published Online:: 11 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2603
Pages:: 1441–1459

Abstract

Out of the enormous branches of mathematics, graph theory plays a vital role in the fields of applied mathematics and scientific computing. One of the major fields of graph theory is the study of graph labeling problems. The present work involves the graceful labeling of a cycle of length three by joining isomorphic copies of paths to all of its vertices. The present work also analyzes the design of graceful graphs, which are created by joining caterpillars with either one or two end vertices of a cycle. Further, it establishes graceful labeling by joining two hairy cycle graphs with a common edge. To find all the results in this paper, the inverse transformation technique is used.

Keywords

Graceful labeling Path Cycle Caterpillar Inverse transformation Unicyclic graphs

Subject Classifications

05C7805C1005C38

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