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    BOUNDS ON SPLIT TOTAL DOMINATION NUMBER OF GRAPHS
    (ADV MATH SCI JOURNALAdvances in Mathematics: Scientific Journal 9 (2020), no.3, 831–837, 2020) Brindha T; Subiksha R
    A dominating set for a graph G = (V,E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number (G) is the number of vertices in a smallest dominating set for G. In this paper a new parameter, split total dominating Set D has been introduced. A dominating set is called split total dominating set if is disconnected and every vertex v in V is adjacent to an element of D. The split total domination number is given by st(G). We considered the split total domination number of some undirected graphs, non-trivial, connected, and finite. The bounds for split total domination number and the Nordhaus-Gaddum type results on split total domination number has been discussed. Also a few results on split total domination numbers have been obtained.
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    A NEW HYBRID APPROACH TO TRAVELLING SALESMAN PROBLEM BY REINFORCEMENT LEARNING AND IMPROVEMENT BY TWO-OPT ALGORITHM
    (The Seybold Report, 2023-03-30) Brindha T; Saurabhee, Sakthivel
    Travelling Salesman Problem is a well-known problem in combinatorial optimization theory that is still being extensively studied up to date. Various approaches have been analyzed and developed to find an optimal solution to this problem. This paper focuses on a new hybrid approach to the Travelling Salesman Problem using Reinforcement Learning and its improvement by Two-Opt algorithm. The proposed algorithm has been applied to three real world problems, which are the three South Indian states namely, Tamil Nadu, Kerala and Andhra Pradesh which has 32, 16 and 27 cities respectively. The proposed algorithm is also compared to the classical algorithms, especially the Two- Opt algorithm to analyse and find the best of the two given here
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    REGULAR PANCYCLIC GRAPHS OF SET DOMINATION AND TOTAL SET DOMINATION
    (Journal of Adv Research in Dynamical & Control Systems, 2017) Sumathi P; Brindha T
    Let G=(V,E) be a simple, undirected, finite nontrivial graph. A dominating set S is a set dominating set of G if for every set T⊆V-S, there exists a non-empty set R⊆S such that the subgraph is connected. A dominating set S is called a total set dominating set if the following conditions hold: (i) every vertex of V(G) is adjacent to some vertex in S (ii) for every set T⊆V-S there exists a non-empty set R⊆S such that the subgraph is connected. In this paper, we establish that for all n≥3 there exists a k-regular pancyclic graph G with n vertices and γs(G)= γts(G) where both n and k are even and 6≤k≤n-1. And, there exists a k-regular pancyclic graph G with n vertices and γs(G)= γts(G) where n is even and k is odd and 5≤k≤n-1. Also, we establish that, there exists a n-regular (n=3,4) graph G with the property that γs(G)= γts(G
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    SUBDIVISION NUMBER OF SPLIT POINT SET DOMINATION OF A GRAPH
    (The Seybold Report, 2023) Brindha T
    Let G= (V,E) be a connected, nontrivial, simple, finite graph. In this paper a new parameter called subdivision split point set domination is introduced and is defined by a set D of vertices in a graph G is a subdivision point set domination, if (i) The graph obtained from a graph G by subdividing each edge of G exactly once (ii) For every set S⊆ V-D such that v∈ D, that is is connected. (iii) The induced sub graph is disconnected.The minimum cardinality of subdivision split point set dominating set is denoted by sp (S (G)). Besides some bounds, exact values of sp(S (G)) are determined. Some theorems based on split point Set Domination are also discussed.