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Journal articles on the topic 'Equitable total coloring'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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1

Rupam, Shrivastava, and Dr. Satish Agnihotri Prof. "A Study on the Total Coloring and Equitable Total Coloring for Splitting Graph." International Journal of Contemporary Research in Multidisciplinary 3, no. 5 (2024): 137–42. https://doi.org/10.5281/zenodo.13862782.

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This study focuses on the total coloring and equitable total coloring of splitting graphs, an area of graph theory that examines the assignment of colors to both vertices and edges under specific constraints. Total coloring involves assigning distinct colors to adjacent or incident elements (vertices and edges) in such a way that no two adjacent or incident elements share the same color. Equitable total coloring further requires the distribution of colors across vertices and edges to be as balanced as possible. The splitting graph, derived from a base graph by splitting its vertices, presents
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2

R. Sudhakar. "Equitable Total Coloring of Line Graph of Certain Graphs." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2370–79. https://doi.org/10.52783/cana.v32.4524.

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An equitable total-coloring of a graph G is a proper total-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determined the equitable total chromatic number for line graph of ladder, slanting ladder, triangular snake, alternate triangular snake, quadrilateral snake and alternate quadrilateral snake Introduction: Graph coloring is a fundamental problem in graph theory with applications in scheduling, networking, and resource allocation. A total-coloring of a graph G is an assignment of colors to both vertices and edges such tha
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3

Kaul, Hemanshu, Jeffrey A. Mudrock, and Michael J. Pelsmajer. "Total Equitable List Coloring." Graphs and Combinatorics 34, no. 6 (2018): 1637–49. http://dx.doi.org/10.1007/s00373-018-1965-x.

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4

Gonçalves, Isabel F. A., Simone Dantas, and Diana Sasaki. "On equitable total coloring of snarks." Procedia Computer Science 195 (2021): 334–42. http://dx.doi.org/10.1016/j.procs.2021.11.041.

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5

Tong, Chunling, Lin Xiaohui, Yang Yuansheng, and Li Zhihe. "Equitable total coloring of Cm□Cn." Discrete Applied Mathematics 157, no. 4 (2009): 596–601. http://dx.doi.org/10.1016/j.dam.2008.08.030.

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6

Gui, Hao, Weifan Wang, Yiqiao Wang, and Zhao Zhang. "Equitable total-coloring of subcubic graphs." Discrete Applied Mathematics 184 (March 2015): 167–70. http://dx.doi.org/10.1016/j.dam.2014.11.014.

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7

Gong, Kun, Zhong-fu Zhang, and Jian-fang Wang. "Equitable total coloring of F n ⋁ W n." Acta Mathematicae Applicatae Sinica, English Series 25, no. 1 (2008): 83–86. http://dx.doi.org/10.1007/s10255-006-6031-4.

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8

Lozano, Abel Rodolfo García, Angelo Santos Siqueira, Clícia Valladares Peixoto Friedmann, and Samuel Jurkiewicz Jurkiewicz. "RELATIONSHIP BETWEEN EQUITABLE TOTAL COLORING AND RANGE COLORING IN SOME REGULAR GRAPHS." Pesquisa Operacional 36, no. 1 (2016): 101–11. http://dx.doi.org/10.1590/0101-7438.2016.036.01.0101.

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9

Huanping, Zhao, Xue Dangqin, and Shi Huojie. "Strong Vertex-distinguishing Total Coloring Algorithm for Complete Graphs based on Equitable Coloring." Journal of Engineering Science and Technology Review 13, no. 1 (2020): 126–32. http://dx.doi.org/10.25103/jestr.131.17.

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10

Wang, Wei-Fan. "Equitable Total Coloring of Graphs with Maximum Degree 3." Graphs and Combinatorics 18, no. 3 (2002): 677–85. http://dx.doi.org/10.1007/s003730200051.

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11

Akbar, M. M. Ali, K. Kaliraj, and J. Vernold Vivin. "On Equitable Coloring of Central Graphs and Total Graphs." Electronic Notes in Discrete Mathematics 33 (April 2009): 1–6. http://dx.doi.org/10.1016/j.endm.2009.03.001.

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12

Vernold Vivin, J., K. Kaliraj, and M. M. Akbar Ali. "Equitable Coloring on Total Graph of Bigraphs and Central Graph of Cycles and Paths." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–5. http://dx.doi.org/10.1155/2011/279246.

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The notion of equitable coloring was introduced by Meyer in 1973. In this paper we obtain interesting results regarding the equitable chromatic number for the total graph of complete bigraphs , the central graph of cycles and the central graph of paths .
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13

Jose, Sabitha, and Sudev Naduvath. "Further Results on Equitable Near Proper Coloring of Derived Graph Families." Utilitas Mathematica 121, no. 1 (2024): 53–68. https://doi.org/10.61091/um121-05.

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A proper coloring assigns distinct colors to the adjacent vertices of a graph. An equitable near proper coloring of a graph G is an improper coloring in which neighbouring vertices are allowed to receive the same color such that the cardinalities of two distinct color classes differ by not more than one and the number of monochromatic edges is minimised by giving certain restrictions on the number of color classes that can have an edge between them. This paper discusses the equitable near proper coloring of line, middle, and total graphs of certain graph classes, such as paths, cycles, sunlet
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14

Aliyar, S. Moidheen, S. Manimaran, and K. Manikandan. "Equitable Total Coloring of Direct Product of Path and Cycle." Journal of Computer and Mathematical Sciences 10, no. 7 (2019): 1476–81. http://dx.doi.org/10.29055/jcms/1137.

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15

da Silva, A. G., S. Dantas, and D. Sasaki. "Equitable total coloring of complete r-partite p-balanced graphs." Discrete Applied Mathematics 261 (May 2019): 123–35. http://dx.doi.org/10.1016/j.dam.2018.03.009.

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16

Aliyar, S. M., K. Manikandan, and S. Manimaran. "AN EQUITABLE TOTAL COLORING OF SOME CLASSES OF PRODUCT OF GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 10 (2020): 8357–65. http://dx.doi.org/10.37418/amsj.9.10.65.

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17

Veninstine Vivik, J., and P. Xavier. "ESTIMATION OF EQUITABLE TOTAL COLORING OF SPLITTING ON DOUBLE WHEEL AND SUNLET GRAPHS." Advances in Mathematics: Scientific Journal 10, no. 2 (2020): 869–77. http://dx.doi.org/10.37418/amsj.10.2.16.

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18

Palma, Miguel, Isabel Gonçalves, Diana Sasaki, and Simone Dantas. "On total coloring and equitable total coloring of infinite snark families." RAIRO - Operations Research, September 5, 2023. http://dx.doi.org/10.1051/ro/2023129.

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We show that all members of the SemiBlowup, Blowup and the first Loupekine snark families have equitable total chromatic number equal to 4. These results provide evidence of negative answers for the questions proposed: by Cavicchioli et al. (2003) about the smallest order of a Type 2 snark of girth at least 5; and by Dantas et al. (2016) about the existence of Type 1 cubic graph with girth at least 5 and equitable total chromatic number 5. Moreover, we show new infinite families of snarks obtained by the Kochol superpositions that are Type 1.
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19

Girija.G and Vivik.J Veninstine. "Equitable Total Coloring of Some Graphs." April 21, 2015. https://doi.org/10.5281/zenodo.815703.

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20

Furmańczyk, Hanna, and Rita Zuazua. "Equitable total coloring of corona of cubic graphs." Discussiones Mathematicae Graph Theory, 2019. http://dx.doi.org/10.7151/dmgt.2245.

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21

Araujo, Rieli, and Diana Sasaki. "On the equitable total coloring of Loupekine snarks." Matemática Contemporânea 55, no. 14 (2023). http://dx.doi.org/10.21711/231766362023/rmc5514.

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22

da Silva, Anderson, S. Dantas, and Diana Sasaki. "On equitable total coloring of complete r-partite graphs." Matemática Contemporânea 45, no. 16 (2017). http://dx.doi.org/10.21711/231766362017/rmc4516.

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23

Veninstine Vivik, J., and D. Dafik. "Splitting on classes of helm graphs and its equitabletotal chromatic number." Advances in Mathematics: Scientific Journal, May 21, 2020, 635–42. http://dx.doi.org/10.37418/amsj.9.2.12.

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The equitable total coloring of a graph $G$ is the different colors used to color all the vertices and edges of $G$, in the order that adjacent vertices and edges are assigned with least different $k$-colors and can be partitioned into colors sets which differ by maximum one. The minimum of $k$-colors required is known as the equitable total chromatic number. In this paper the splitting graph of Helm and Closed Helm graph is constructed and its equitable total chromatic number is acquired.
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24

Marsh, Max, Jeffrey A. Mudrock, and Tim Wagstrom. "On list equitable total colorings of the generalized theta graph." Discussiones Mathematicae Graph Theory, 2020. http://dx.doi.org/10.7151/dmgt.2292.

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