Strong Domination Polynomials of Queen Crown Graph

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-2
Year of Publication : 2020
Authors : S.Angelin Kavitha Raj, S.Jeya Mangala Abirami
  10.14445/22315373/IJMTT-V66I2P510

MLA

MLA Style:S.Angelin Kavitha Raj, S.Jeya Mangala Abirami   "Strong Domination Polynomials of Queen Crown Graph" International Journal of Mathematics Trends and Technology 66.2 (2020):99-104. 

APA Style: S.Angelin Kavitha Raj, S.Jeya Mangala Abirami(2020). Strong Domination Polynomials of Queen Crown Graph International Journal of Mathematics Trends and Technology, 99-104.

Abstract
Let G=(V,E) be a simple graph. A set S ⊆ V is called a dominating set if every vertex v ∈ V is either a member of S or adjacent to a member of S. A set S ⊆ V is a Strong dominating set of G if for every vertex v ∈ V-S there exists a u ∈ S such that uv ∈ E and deg(u) ≥ deg(v). Let Qm,n be a Queen crown graph which is obtained from two null graphs of order zero and taking one copy of null graph G1 with m vetices , m ≥ 3 and another copy of null graph G2 with n=2 vertices (that should be fixed) then joining the vertex of G1 with an edge to every vertex of G2. Let Sd(Qjm,n) be the family of strong dominating set of Queen crown graph with number of elements in the set j and let Sd(Qm,n,j) =|Sd(Qjm,n). In this paper we establish Qm,n nd obtain a iterative formula for Sd(Qjm,n). Using this iterative formula we consider the polynomial for SD (Qm,n,X)= Σj=1m+n-1[(m+n-1)/j - (m+n-2)/j ]xj+1 Also we have determine several properties of polynomials on Queen crown graphs.

Reference
[1] S.Alikhani,Y.H.Peng, Dominating sets and Domination Polynomials of Cycles, Global Journal of Pure and Applied Mathematics, 4 No.2,151-162(2008)
[2] S.Alikhani,Y.H.Peng, Dominating sets and Domination Polynomials of Certain graphs II Opuscula Mathematics 30No.1,37-51(2010)
[3] Sahib Shayyal Kahat,Abdul Joli M. Khalaf, Dominating sets and Domination Polynomial of stars , Australian Journal of Basic and Applied Science ,8 no.6, 383-386(2014)
[4] Sahib Shayyal Kahat,Abdul Joli M. Khalaf, Dominating sets and Domination Polynomial of wheels, Australian Journal of Basic and Applied Science
[5] S.Angelin Kavitha Raj and Robinson Chelladurai, Weak dominating sets and Weak domination Polynomial of complete graph ,Journal of Computer and Mathematical SciencesVol9(12),2138-2146 December 2018

Keywords
Strong dominating set , Strong domination polynomial , Queen crown graph