International Journal of Mathematics Trends and Technology
Volume 66 | Issue 2 | Year 2020 | Article Id. IJMTT-V66I2P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I2P510
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.
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S.Angelin Kavitha Raj, S.Jeya Mangala Abirami, "Strong Domination Polynomials of Queen Crown Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 2, pp. 99-104, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I2P510
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