The Multipartite Property and the Cycle Structure of the Graph Associated with the Elements of Unequal Order in the Group (Zn,⊕)

Authors

  • Shaik Shahida Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India Author
  • Madhavi Levaku Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India Author
  • Chalapathi Tekuri Assistant Professor, Department of Mathematics, Madanapalle Institute of Technology & Science (MITS), Deemed to be University, Madanapalle-517325, Andhra Pradesh, India Author
  • Ramya Thejeswini Kammara Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India Author

DOI:

https://doi.org/10.47363/JMCA/2026(5)247

Keywords:

Complete Graph, Component of a Graph, Multipartite Graph, Hamiltonian Property, Triangle

Abstract

The first two authors have introduced a new class of graphs  associated with the elements of unequal order in the group  of residue classes modulo , an integer. It is established that it is a connected graph and the vertex degree and size of the graph  are determined. In this paper, it is shown that  is Hamiltonian if  is even. Further, it is proved that it is not a complete graph and it is a complete multipartite graph. The formula for the number of triangles in  is determined.

Author Biographies

  • Shaik Shahida, Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

    Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

  • Madhavi Levaku, Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

    Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

  • Chalapathi Tekuri, Assistant Professor, Department of Mathematics, Madanapalle Institute of Technology & Science (MITS), Deemed to be University, Madanapalle-517325, Andhra Pradesh, India

    Assistant Professor, Department of Mathematics, Madanapalle Institute of Technology & Science (MITS), Deemed to be University, Madanapalle-517325, Andhra Pradesh, India

  • Ramya Thejeswini Kammara, Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

    Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, Andhra Pradesh, India

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Published

2026-09-24

Issue

Vol. 5 No. 5 (2026): Volume 5 Issue 5

Section

Articles