Introduction to dominated edge chromatic number of a graph

• Autorzy: Piri Mohammad R. , Alikhani Saeid

Identyfikatory

DOI

10.7494/OpMath.2021.41.2.245

• Języki publikacji: EN

Abstrakty

EN

We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph G, is a proper edge coloring of G such that each color class is dominated by at least one edge of G. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by [formula]. We obtain some properties of [formula] and compute it for specific graphs. Also examine the effects on [formula] when G is modified by operations on vertex and edge of G. Finally, we consider the k-subdivision of G and study the dominated edge chromatic number of these kind of graphs.

Słowa kluczowe

EN

dominated edge chromatic number; subdivision; operation; corona

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 2
• Strony: 245--257
• Opis fizyczny: BIbliogr. 17 poz.

Twórcy

autor

Piri Mohammad R.

• Yazd University Department of Mathematics 89195-741, Yazd, Iran

autor

Alikhani Saeid

• Yazd University Department of Mathematics 89195-741, Yazd, Iran

• https://orcid.org/0000-0002-1801-203X

Bibliografia

• [1] S. Alikhani, E. Deutsch, More on domination polynomial and domination root, Ars Combin. 134 (2017), 215-232.
• [2] S. Alikhani, M.R. Piri, Dominated chromatic number of some operations on a graph, arXiv:1912.00016 [math.CO].
• [3] S. Alikhani, S. Soltani, Distinguishing number and distinguishing index of neighbourhood coronal of two graphs, Contrib. Discrete Math. 14 (2019), no. 1, 175-189.
• [4] S. Alikhani, S. Soltani, Distinguishing number and distinguishing index of natural and fractional powers of graphs, Bull. Iran. Math. Soc. 43 (2017), no. 7, 2471-2482.
• [5] S. Alikhani, S. Soltani, Trees with distinguishing number two, AKCE International J. Graphs Combin. 16 (2019), 280-283.
• [6] F. Choopani, A. Jafarzadeh, D.A. Mojdeh, On dominated coloring of graphs and some Nardhaus-Gaddum-type relations, Turkish J. Math. 42 (2018), 2148-2156.
• [7] R. Gera, S. Horton, C. Ramussen, Dominator colorings and safe clique partitions, Conress. Num. 181 (2006), 19-32.
• [8] N. Ghanbari, S. Alikhani, More on the total dominator chromatic number of a graph, J. Inform. Optimiz. Sci. 40 (2019), no. 1, 157-169.
• [9] N. Ghanbari, S. Alikhani, Total dominator chromatic number of some operations on a graph, Bull. Comp. Appl. Math. 6 (2018), no. 2, 9-20.
• [10] N. Ghanbari, S. Alikhani, Introduction to total dominator edge chromatic number, TWMS J. App. Eng. Math. (to appear).
• [11] B. Grunbaum, Acyclic coloring of planar graphs, Israel J. Math. 14 (1973), 390-408.
• [12] A.V. Kostochka, M. Mydlarz, E. Szemeredi, H.A. Kierstead, A fast algorithm for equitable coloring, Combinatorica 30 (2010), no. 2, 217-224.
• [13] V.R. Kulli, D.K. Patwari, On the total edge domination number of graph, [in:] A.M. Mathi (ed.), Proc. of the Symp. on Graph Theory and Combinatorics, Kochi Centre Math. Sci, Trivandrum, Series Publication 21 (1991), 75-81.
• [14] H.B. Merouane, M. Chellali, M. Haddad, H. Kheddouci, Dominated coloring of graphs, Graphs Combin. 31 (2015), 713-727.
• [15] M. Walsh, The hub number of a graph, Int. J. Math. Comput. Sci. 1 (2006), 117-124.
• [16] X. Zhu, Circular chromatic number: a survey, Discrete Math. 229 (2001), 371-410.
• [17] X. Zhou, T. Nishizeki, S. Nakano, Edge-coloring algorithms, Technical report, Graduate School of Information Sciences, Tohoku University, Sendai 980-77, Japan, 1996.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).