Burning, edge burning & chromatic burning classification of some graph family

Komala, S.; Mary, U.

doi:10.47974/JDMSC-1911

Open Access Research Article

Burning, edge burning & chromatic burning classification of some graph family

S. Komalakomalaojas1@gmail.comDepartment of MathematicsNirmala College for Women (Autonomous)Coimbatore, Tamil Nadu, 641018, IndiaView full profile → , ^*U. MaryCorresponding authorumarycbe@gmail.comDepartment of MathematicsNirmala College for Women (Autonomous)Coimbatore, Tamil Nadu, 641018, IndiaView full profile →

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pp. 665–674Vol. 27Issue 2-BMarch 2024DOI: 10.47974/JDMSC-1911 Crossmark XML

Published Online:: 11 Apr 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1911
Pages:: 665–674

Abstract

Graph ‘G’ is a Simple and undirected graph, which has a lowest number of color that is required to color the edge is called chromatic index. It is denoted by the symbol χ1(G). In order to burn a graph, a minimum source of edges is required which is called edge burning index or edge burning number and it is denoted by the symbol b1(G). A minimum cardinality of color graph set and the source of the burning index set are called edge chromatic burning and let us assume that it is represented by the symbol χb1(G). In this paper we are mainly concentrating on identifying the chromatic burning and edge chromatic burning graphs and their chromatic burning index using a specific graph family. They are Petersen graph, Helm graph and n- Sunlet graph.

Keywords

Burning Edge burning Chromatic burning number Edge chromatic burning index

Subject Classifications

05C1505C99

References

[1] Anthony Bonato, Jeannettejanseen and Elham Roshanbin, “How to burn a graph”, arXiv:1507.06524 [math.Co], pg 01, 23’ july (2015).
[2] Douglas B.West, “Introduction to Graph theory, Second edition”, PHI Learning Private Limited, pg no : 274 (2021).
[3] Gary Chartrand & Pingzhang, “A first course in Graph theory”, Dover Publications, INC. Garden City, New York, pg no : 269.
[4] Gee-Choon Lau, Wai-Chee shiu & Chee-Xian Soo , “On local antimagic chromatic number of spider graphs”, Journal of Discrete Mathematical Sciences and Cryptography, 7, March (2022). DOI: 10.1080/09720529.2021.1892270.
[5] Komala S & Mary U, “Burning number for a few graphs using the line graph medium”, Research and Reflections on Education ISSN 0974-648X(P) Vol. 20 No. 3A, 61-66 October (2022).
[6] Komala S & Mary U, “ Chromatic Burning of Certain Graphs”, International journal of Creative Research thoughts,Volume 10, issue 04 April (2022), ISSN: 2320-2882.
[7] Mary U and Joseph Paul R, “A study on geo Chromatic Number of Some Graphs Families”, International journal of Scientific research in Mathematical and Statistical Sciences, Volume-9, Issue-5, pp.01-06, October (2022).
[8] Narsingh deo, “Graph theory with applications to Engineering & computer science” , PHI Learning Private Limited, pg no : 1 (2021).
[9] M.Nalliah, R.Shankar & Tao-Ming Wango, “Local antimagic vertex coloring for generalized friendship graphs”, Journal of Discrete Mathematical Sciences and Cryptography, 29, March (2022). DOI: 10.1080/09720529.2021.1974651.
[10] Kumar, Anil, Gupta, Amit Kumar, Panwar, Deepak , Chaurasia, Sandeep & Goyal, Dinesh. Operating system security with discrete mathematical structure for secure round robin scheduling method with intelligent time quantum, Journal of Discrete Mathematical Sciences and Cryptography, 26:5, 1519–1533 (2023).
[11] Kushwaha, Satpal Singh, Joshi, Sandeep & Gupta, Amit Kumar. An efficient approach to secure smart contract of Ethereum blockchain using hybrid security analysis approach, Journal of Discrete Mathematical Sciences and Cryptography, 26:5, 1499–1517 (2023), DOI: https://doi.org/10.47974/JDMSC-1815.
[12] Joshi, Ruchi, Mathur, Priya, Gupta, Amit Kumar, Singh, Suyesha, Paliwal, Vismita & Nayar, Sejal. Mathematical modeling of intelligent system for predicting effectiveness of premenstrual syndrome, Journal of Interdisciplinary Mathematics, 26:3, 551-562 (2023).

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