The Forcing Steiner Hop Domination Number of a Graph
Keywords:
Steiner number, hop domination number, Steiner hop domination number, forcing Steiner hop domination number.Abstract
Let W is a γ_hs-set of G. A subset T of W is called a forcing subset of W if W is the unique γ_hs-set containing T. The minimum cardinality of T is the forcing Steiner hop domination number of W and is denoted by f_(γ_hs ) (G). The forcing Steiner hop domination number of G is f_(γ_hs ) (G)= min {f_(γ_hs ) (G)}, where the minimum is taken over all γ_hs-sets of G. It is shown that for every pair of integers a and b with 0 ≤ a ≤ b and b≥ a+2, there exists a connected graph G such that f_(γ_hs ) (G)=a and γ_hs (G)=b.
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D. Anusha, J. John and S. Joseph Robin, Graphs with small and large hop domination numbers, Bulletin of the international mathematical virtual institute, 11(3), (2021), 483-480.
D. Anusha, S. Joseph Robin and J. John, Further results on the hop domination number of a graph, Boletim Da Sociedade Paranaense de Matemática, 42, (2024), 1-12.
F. Buckley and F. Harary, Distance in Graphs, Addition - Wesley Publishing Company, Redwood City, California, 1990.
G. Chartrand and P. Zhang, The Steiner number of a graph, Discrete Mathematics, 242, (2002), 41-54.
S. Gomathi Radha, K. Ramalakshmi and A. Mahalakshmi, Strong hop Steiner Domination in graphs, International Journal of Creative Research Thoughts (IJCRT), 12(4), (2024), d590-d595.
Ignacio M Pelayo, Comment on "The Steiner number of a graph”, Discrete Mathematics, 280 (1-3), (2004), 259-263.
J. John and S. Ancymary, The edge-to-vertex Steiner domination number of a graph, TWMS Journal of Applied and Engineering Mathematics, 12(4), (2022), 1311-1321.
J. John and M.S. Malchijah Raj, On the complement connected Steiner number of a graph, Acta Mathematica Universitatis Comenianae, 90(4), (2021), 377-386.
J. John and M. S. Malchijah Raj, The forcing nonsplit domination number of a graph, The Korean Journal of Mathematics, 29 (1) (2021), 1-12.
C. Natarajan and S.K. Ayyaswamy, Hop domination sets in graphs-II, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, (ASUOC), 23(2), (2015), 187-199.
A.P. Santhakumaran and J. John, The forcing Steiner number of a graph, Discussiones Mathematicae Graph Theory, 31(1), (2011), 171-181.
A. Siva Jothi, J. John and S. Robinson Chellathurai, The forcing edge Steiner number of a graph, International Jounral of Pure and Applied Mathematics, 119(4), (2018), 695-704.
S.K. Vaidya and S.H. Karkar, Steiner domination number of some graphs, International Journal of Mathematics and Scientific Computing, 5(2), (2015), 1-3.
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