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On $$\alpha $$-Split Domination in Graphs
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2022In this paper, we present the concept of alpha-split domination in graphs. Besides, we calculate the alpha-split domination number of path, cycle, complete bipartite graphs and discuss the upper bounds for a-split domination number in terms of order p, size q and the maximum degree d.
S. Amutha +4 more
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Split domination number of divisible dominating graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2020A graph G is a divisible dominating graph if the vertices are labeled with positive integers d and n except 0, such that the vertex labeled with n is adjacent to the vertex named with d if and only...
S. Amutha +3 more
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Vector Domination in split-indifference graphs
Information Processing Letters, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rodrigo Lamblet Mafort, Fábio Protti
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Conditions for dominated splittings
Acta Mathematica Sinica, English Series, 2009Let \(M\) be an \(m\)-dimensional closed manifold (\(m\geq 2\)) and \(\text{Diff}^1(M)\) be the space of diffeomorphisms of \(M\) endowed with the \(C^1\) topology. For \(f\in\text{Diff}^1(M)\), let \(\Lambda\) be its compact invariant set. A \(Df\)-invariant splitting \(T_{\Lambda}M=E\oplus F\) is called a dominated splitting of index \(i\) over ...
Liu, Geng, Liang, Chao
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THE DOMINATION GAME ON SPLIT GRAPHS
Bulletin of the Australian Mathematical Society, 2018We investigate the domination game and the game domination number $\unicode[STIX]{x1D6FE}_{g}$ in the class of split graphs. We prove that $\unicode[STIX]{x1D6FE}_{g}(G)\leq n/2$ for any isolate-free $n$-vertex split graph $G$, thus strengthening the conjectured $3n/5$ general bound and supporting Rall’s $\lceil n/2\rceil$-conjecture.
TIJO JAMES +2 more
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Pinball billiards with dominated splitting
Ergodic Theory and Dynamical Systems, 2009AbstractWe study the dynamics of a type of non-conservative billiards where the ball is ‘kicked’ by the wall giving a new impulse in the direction of the normal. For different types of billiard tables we study the existence of attractors with dominated splitting.
Markarian, Roberto +2 more
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Dominated splitting versus small angles
Acta Mathematica Sinica, English Series, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Chao, Liu, Geng
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Independent Domination of Splitted Graphs
International Journal of Mathematics Trends and Technology, 2014A dominating set D of a splitted graph S(G) = ( V, E ) is an independent dominating set if the induced subgraph has no edges. The independent domination number i[S(G)] of a graph S(G) is the minimum cardinality of an independent dominating set.
A.Nellai Murugan, A.Esakki muthu
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Detour global domination for splitting graph
Discrete Mathematics, Algorithms and Applications, 2022In this paper, we introduced the new concept detour global domination number for splitting graph of standard graph. The detour global dominating sets in some standard and special graphs are determined. First we recollect the concept of splitting graph of a graph and we produce some results based on the detour global domination number of splitting ...
Jayasekaran, C., Ashwin Prakash, S. V.
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TOTAL DOMINATION POLYNOMIALS OF SOME SPLITTING GRAPHS
Advances and Applications in Discrete Mathematics, 2017Summary: A hypergraph is an ordered pair \(H=(V,E)\), where \(V\) is a finite nonempty set called vertices and \(E\) is a collection of subsets of \(V\), called hyperedges or simply edges. A subset \(T\) of vertices in a hypergraph \(H\) is called a vertex cover if \(T\) has a nonempty intersection with every edge of \(H\). The vertex covering number \(
Latheeshkumar, A. R., Kumar, V. Anil
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