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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 | ||
| Gracelin Goldy J V* 1؛ Lal Gipson K2 | ||
| 1Department of Mathematics, Scott Christian College (Autonomous), Nagercoil - 629 003, Kanyakumari District, Tamilnadu, India. (Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627 012 | ||
| 2Department of Mathematics, Scott Christian College(Autonomous),Nagercoil-629003.Affilliated to Manonmanium Sundaranar University,Abishekapatti,Tirunelveli-627012 | ||
| 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 | ||
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