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On Irregular Colorings of Unicyclic Graph Family
Abstract
Irregular coloring is a proper coloring and each vertex on a graph must have a different code. The color code of a vertex v is where and is the number of vertices that are adjacent to v and colored i. The minimum k-color used in irregular coloring is called the irregular chromatic number and denoted by . In this paper, we discuss the irregular chromatic number for the bull graph, pan graph, sun graph, peach graph, and caveman graph.
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K. Anitha, B. Selvam, and K. Thirusangu. New Irregular Colourings of Graphs. Journal of Applied Science and Computations. vol. 6, no.5, pp.269-279,2019.
P. Zhang. A Kaleidoscopic View of Graph Colorings (Springer Nature), 2016.
M. Radcliffe and P. Zhang. Irregular Coloring of Graphs. Kalamazoo: Western Michigan University. 2005.
A. Rohini and M. Venkatachalam. On Irregular Colorings of Double Wheel Graph Families. International Conference on Current Scenario in Pure and Applied Mathematics. vol 68, no. 1, pp. 944-949, 2019.
A. Rohini and M. Venkatachalam. On irregular colorings of fan graph families. International Conference on Applied and Computational Mathematics. 1139, pp 1-6, 2018.
Rohini, A., and M. Venkatachalam. On irregular coloring of wheel related graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics68.2 (2019): 1462-1472.
R. Avudainayaki, B. Selvam, and K. Thirusangu. Irregular Coloring of Some Classes of Graphs. International Journal of Pure and Applied Mathematics. vol.100, no.10, pp.119-127, 2016.
M. Anderson, R. P. Vitray, and J. Yellen. Irregular colorings of regular graphs. Discrete Mathematics. 312. pp. 2329-2336, 2012.
A. I. Kristiana, R. Alfarisi, Dafik, & N. Azahra, Local irregular vertex coloring of some families graph. Journal of discrete mathematical sciences and cryptography, 25(1), 2022, 15-30.
Q. A’yun, R. Adawiyah, I. H. Agustin, & E.R. Albirri, On the irregular coloring of bipartite graph and tree graph families. In Journal of Physics: Conference Series (Vol. 1836, No. 1, p. 012024). 2021. IOP Publishing.
R. Saraladevy, P. Nedumaran, and K. Anitha. Irregular set coloring of star families. AIP Conference Proceedings. Vol. 2261. No. 1. AIP Publishing LLC, 2020.
A. Rohini, and M. Venkatachalam. On Irregular Coloring of Some Generalised Graphs. Advanced Studies in Contemporary Mathematics 30.1 (2020): 99-120.
R. Avudainayaki, B. Selvam, K. Thirusangu, & P. P. Ulaganathan, P. P. Irregular Coloring in Mycielskian Graphs. Recent Trends in Graph Theory & Combinatorics, 14. 2017.
P. Ghosh, S. N. Mishra, and A. Pal. Various Labeling on Bull Graph and some Related Graphs. International Journal of Applications of Fuzzy Sets and Articial Intelligence. 5, pp.23-35, 2015.
Helmi, F. Fran, and D. R. Putra. Prime Labeling of Pan Graph and Its Line, Middle and Duplication Graph. PRISMA. vol.3, pp.8-13, 2020.
M. Mirzakhah and D. Kiani. The Sun Graph is Determined by Its Signless Laplacian Spectrum. Electronic Journal of Linear Algebra. 20, pp.610-620, 2010.
B. H. Xing, G. D. Yu, L. X. Wang and J Cao. The Harary Index of All Unicyclic Graphs with Given Diameter. Discrete Dynamics in Nature and Society. pp. 1-6, 2018.
D. Koutra. Exploring and Making Sense of Large Graphs. Pittsburgh. Computer Science Department. Carnegie Mellon University, 2015.
DOI: https://doi.org/10.18860/ca.v7i4.16917
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