Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 62: Issue 1
Total Coloring of the Generalized Corona Product of Graphs
Authors:
T. Kavaskar Department of Mathematics, Central University of Tamil Nadu, Thiruvarur - 610 005, INDIA

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Sreelakshmi Sukumaran Department of Mathematics, Central University of Tamil Nadu, Thiruvarur - 610 005, INDIA

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Pages:
1–6
Online Publication Date:
17 Mar 2025
Publication Date:
09 Apr 2025
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2025.04326
Keywords:
Total coloring conjecture; Generalized Corona Product
Restricted access

A long standing Total Coloring Conjecture (TCC) asserts that every graph is total colorable using its maximum degree plus two colors. A graph is type-1 (or type-2) if it has a total coloring using maximum degree plus one (or maximum degree plus two) colors. For a graph 𝐺 with 𝑚 vertices and for a family of graphs {𝐻1, 𝐻2, … , 𝐻𝑚}, denote G∘˜Λi=1mHi, the generalized corona product of 𝐺 and 𝐻1, 𝐻2, … , 𝐻𝑚. In this paper, we prove that the total chromatic number of G∘˜Λi=1mHi is the maximum of total chromatic number of 𝐺 and maximum degree of G∘˜Λi=1mHi∈ plus one. As an immediate consequence, we prove that G∘˜Λi=1mHi is type-1 when 𝐺 satisfies TCC and also the corona product of 𝐺 and 𝐻 is type-1 if 𝐺 satisfies TCC. This generalizes some results in (R. Vignesh. et. al. in Discrete Mathematics, Algorithms and Applications, 11(1): 2019) and all the results in (Mohan et. al. in Australian Journal of Combinatorics, 68(1): 15-22, 2017.)

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

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Géza TÓTH (Rényi Institute of Mathematics) 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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