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Power Dominator Chromatic Numbers of Splitting Graphs of Certain Classes of Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 12، دوره 9، شماره 2، شهریور 2024، صفحه 317-327 اصل مقاله (389.48 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27744.1337 | ||
| نویسندگان | ||
| K. SATHISH KUMAR* 1؛ GNANAMALAR DAVID2؛ Atulya K Nagar2؛ Subramanian K G2 | ||
| 1Department of Mathematics, Madras Christian College, Chennai 600 059, India | ||
| 2School of Mathematics, Computer Science and Engineering, Liverpool Hope University, Liverpool L16 9JD, UK | ||
| چکیده | ||
| Domination in graphs and coloring of graphs are two main areas of investigation in graph theory. Power domination is a variant of domination in graphs introduced in the study of the problem of monitoring an electric power system. Based on the notions of power domination and coloring of a graph, the concept of power dominator coloring of a graph was introduced. The minimum number of colors required for power dominator coloring of a graph $G$ is called the power dominator chromatic number $\chi_{pd}(G)$ of $G,$ which has been computed for some classes of graphs. Here we compute the power dominator chromatic number for splitting graphs of certain classes of graphs. | ||
| کلیدواژه‌ها | ||
| Splitting Graphs؛ Power domination؛ Coloring | ||
| مراجع | ||
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[1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Elsevier, North Holland, New York, 1986.
[2] J. Deepalakshmi, G. Marimuthu, S. Arumugam, and S. Arumugam, Domination parameters of the splitting graph of a graph, Commun. Comb. Optim. 631–637. https://doi.org/10.22049/cco.2022.27871.1376 [3] P. Dorbec, M. Mollard, S. Klažzar, and S. Špacapan, Power domination in product graphs, SIAM J. Discrete Math. 22 (2008), no. 2, 554–567. http://doi.org/10.1137/060661879 [4] R.M. Gera, On dominator coloring in graphs, Graph Theory Notes of New York 52 (2007), 25–30.
[5] T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning, Domination is graphs applied to electic power networks, SIAM J. Discrete Math. 15 (2002), no. 4, 519–529. https://doi.org/10.1137/S0895480100375831 [6] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs - Advanced Topics, Marcel Dekker. Inc., New York, 1998.
[7] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker. Inc., New York, 1998. [8] S. Muñoz, M. Teresa Ortuño, J. Ramírez, and J. Y´añez, Coloring fuzzy graphs, Omega 33 (2005), no. 3, 211–221. https://doi.org/10.1016/j.omega.2004.04.006 [9] E. Sampathkumar and H.B. Walikar, On splitting graph of a graph, J. Karnatak Univ. Sci. 25 (1980), no. 13, 13–16.
[10] K. Sathish Kumar, N.G. David, and K.G. Subramanian, Graphs and power dominator colorings, Ann. Pure Appl. Math. 11 (2016), no. 2, 67–71.
[11] K. Sathish Kumar, N.G. David, and K.G. Subramanian, Power dominator coloring of certain classes of graphs, International Journal of Creative Research Thoughts 6 (2018), no. 1, 951–954.
[12] K. Sathish Kumar, N.G. David, and K.G. Subramanian, Power dominator coloring of corona graphs, Int. J. Pure Appl. Math. 119 (2018), no. 11, 59–67.
[13] K. Sathish Kumar, N.G. David, and K.G. Subramanian, Power dominator coloring of degree splitting graph of certain graphs, Contemp. Studies Discrete Math. 2 (2018), no. 2, 89–96.
[14] A. Somasundaram and S. Somasundaram, Domination in fuzzy graphs - I, Pattern Recognition Letters 19 (1998), no. 9, 787–791.
[15] A. Uma Maheswari and J. Bala Samuvel, Power dominator coloring for various graphs, Journal of the Maharaja Sayajirao University of Baroda 54 (2020), no. 2, 119–123.
[16] D.B. West, Introduction to Graph Theory, Prentice Hall of India, New Delhi, 2001. | ||
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