LOCAL IRREGULARITY VERTEX COLORING OF BICYCLIC GRAPH FAMILIES

  • Arika Indah Kristiana Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia https://orcid.org/0000-0002-6556-6377
  • Aji Mansur Santoso Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia https://orcid.org/0009-0005-0233-0198
  • Saddam Hussen Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia
  • Edy Wihardjo Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia https://orcid.org/0000-0003-1377-8172
  • Robiatul Adawiyah Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia https://orcid.org/0000-0002-8481-2932
  • Dafik Dafik Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Jember, Indonesia https://orcid.org/0000-0003-0575-3039
DOI: https://doi.org/10.30598/barekengvol19iss2pp1093-1108
Keywords: Bicyclic Graphs, Local Irregularity, Vertex Coloring

Abstract

The graph in this research is a simple and connected graph with  as vertex set and  as an edge set. We used deductive axiomatic and pattern recognition method. Local irregularity vertex coloring is defined as mapping  as vertex irregular -labeling and  where . The conditions for  to be a local irregularity vertex coloring, if  with  as irregularity vertex labeling and for every . The minimum number of colors produced from local irregularity vertex coloring of graph  is called chromatic number local irregularity, denoted by . In this research, we analyze about the local irregularity vertex coloring and determine the chromatic number of local irregularity of bicyclic graphs.

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Published
2025-04-01
How to Cite
[1]
A. I. Kristiana, A. M. Santoso, S. Hussen, E. Wihardjo, R. Adawiyah, and D. Dafik, “LOCAL IRREGULARITY VERTEX COLORING OF BICYCLIC GRAPH FAMILIES”, BAREKENG: J. Math. & App., vol. 19, no. 2, pp. 1093-1108, Apr. 2025.
Issue
Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Arika Indah Kristiana, Aji Mansur Santoso, Saddam Hussen, Edy Wihardjo, Robiatul Adawiyah, Dafik Dafik

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