پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 497 |
| تعداد مقالات | 4,429 |
| تعداد مشاهده مقاله | 7,640,380 |
| تعداد دریافت فایل اصل مقاله | 5,142,091 |
Total outer-connected dominating sets and total outer-connected domination polynomial of complete bipartite graph K2,n | ||
| Journal of Hyperstructures | ||
| دوره 14، شماره 2، اسفند 2025، صفحه 208-216 اصل مقاله (1.41 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.16719.1073 | ||
| نویسندگان | ||
| Lal Gipson K؛ Gracelin Goldy J V* | ||
| Department of Mathematics, Scott Christian College(Autonomous), Nagercoil, Tamil Nadu, India. | ||
| چکیده | ||
| Let G = (V, E) be a simple graph. A set D⊆V (G) is a total outer−connected dominating set of G if D is total dominating, and the induced sub-graph G[V (G) − D] is a connected graph. Let K2,n be the complete bipartite graph and D ̃tc (K2,n,i) denote the family of all total outer-connected dominating sets of K2,n with cardinality i. Let d ̃tc (K2,n,i)=|D ̃tc (K2,n,i)|. In this paper, we obtain recursive formula for d ̃tc (K2,n,i). Using this recursive formula, we construct the polynomial, D~tc (K2,n,x)=∑i=22+nd ̃tc (K2,n,i)xi which we call total outer−connected domination polynomial of K2,n and obtain some properties of this polynomial. | ||
| کلیدواژهها | ||
| Domination؛ Total outer- connected domination؛ Total outer- connected domination number؛ Total outer- connected dominating set؛ Total outer- connected domination polynomial | ||
| مراجع | ||
|
[1] Abel Cabera Martinez, Juan Carlos Hernandez Gomez, Ernesto Parra Inza, Jose Maria Sigarreta Almira, On the total outer K-independent domination number of graphs, Mathematics, 8(2), (2020). [2] I.Beaton, On dominating sets and domination polynomial, library- archieves.Canada.ca,(2021). [3] P.Bosch, E.para Inza, I.Rios Villamar, Total outer- independent domination number:Bounds and algorithms, Algorithms, 18(3), (2025). [4] A. Cabrera Martinez, Total outer- independent domination in regular graphs, Filomat, 38:18, (2024),6581-6586. [5] B. Chaluvaraju, N.Majunath, The co-connected domination polynomial of a graph, 18, (2017), 57-70. [6] J. Cyman, The outer connected domination number of a graph, Australasian journal of combinatorics 38, (2007), 35-46. [7] J. Cyman, Total outer connected domination number in trees, Discuss. Math. Graph theory, 30, (2010), 377-383. [8] J.Cyman, J.Raczek, Total outer-connected domination numbers of trees, Discrete Appl. Math., 157, (2009), 3198-3202. [9] Farshad Kazemnejad, Behanz Pahlavsay, Elisa Palezzato, Michele Torielli, Total outer- connected domination number of middle graphs, arxiv:2308.02127v1, (2023). [10] O.Favaron, H.Karami,S.M. Sheikholeslami, On the total outer-connected domination in graphs, Journal of combinatorial optimization, 27,(2014), 451-461. [11] Frank Harary, Graph Theory, Addison-Wesley Publishing Company, Inc. [12] J. Gross and J. Yellen, Handbook of Graph Theory, CRC Press (2004). [13] T. W. Haynes, S. T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. and Maths, 2, (2013), 267-272. [14] Ihsan. A. Alwan, Ahmed.A. Omran, Domination polynomial of the composition of complete graph and star graph, Journal of physics, Conference series. 1591, (2020). [15] Johannes. H. Hattingh, Ernst.J. Joubert,T.W. Haynes, A note on the total outer-connected domination number of a tree, AKCE International journal of Graphs and Combinatorics, 2, (2010), 223-227. [16] K. Lal Gipson , Subha T, Secure Domination Polynomials Of Paths, International Journal of Scientific and Technology Research, 9 (2), (2020), 6517-6521. [17] Nader Jafari Rad, Lutz Volkman, Generalization of the total outer- connected domination in graphs, RAIRo- Operations Research, 50, (2016), 233-239. [18] Nasrin Jafari, Saied Alikhani, On the roots of total domination polynomial of graphs, (2019), 795-807. [19] B.S. Panda, Arti Pandey,Complexity of total outer- connected domination problem in graphs, Discrete applied mathematics, 199, (2016), 110-122. [20] Saeid Alikhani and Y.H. Peng, Dominating Sets and Domination Polynomials of Paths, International Journal of Mathematics and Mathematical Sciences, 542040, (2009). [21] B.Senthil Kumar, H.Naresh Kumar, Y.B. Venkatakrishnan, Total outer- connected vertex edge domination, Discrete mathematics algorithms and application, 15(1), (2023). [22] A. Vijayan and K Lal Gipson, Dominating Sets of Square of Centipedes, International Journal of Mathematical Archive, 4(2), (2013), 298-310. [23] A. Vijayan and K. Lal Gipson, Dominating Sets and Domination Polynomials of Square of Paths, Open Journal of Discrete Mathematics, 3, (2013), 60-69. | ||
|
آمار تعداد مشاهده مقاله: 297 تعداد دریافت فایل اصل مقاله: 283 |
||