Browsing by Author "Vijayalakshmi, D."

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    A note on dominator chromatic number of line graph and jump graph of some graphs
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Kalaivani, R.; Vijayalakshmi, D.; Other; Other
    A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other color class. In this paper, we obtain the dominator chromatic number for the Line graph of some graphs, Central graph of Line graph of Star graph and Central graph of Line graph of Double Star graph. And also we obtain the dominator chromatic number for J(S_{n}),J(C_{n}) and J(K_{1,n,n,n}) respectively.
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    Degree based topological invariants of splitting graph
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Mohanappriya, G.; Vijayalakshmi, D.; Other; Other
    Topological invariants are the graph theoretical tools to the theoretical chemists, that correlates the molecular structure with several chemical reactivity, physical properties or biological activity numerically. A function having a set of networks(graph, molecular structure) as its domain and a set of real numbers as its range is referred as a topological invariant(index). Topological invariants are numerical quantity of a network that are invariant under graph isomorphism. Topological invariants such as Zagreb index, Randić index and multiplicative Zagreb indices are used to predict the bioactiviy of chemical compounds in QSAR/QSPR study. In this paper, we compute the general expression of certain degree based topological invariants such as second Zagreb index, F-index, Hyper-Zagreb index, Symmetric division degree index, irregularity of Splitting graph. And also we obtain upper bound for first and second multiplicative Zagreb indices of Splitting graph of a graph H, (S′(H)).
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    On achromatic number of central graph of some graphs
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Nithyadevi, N.; Vijayalakshmi, D.; Other; Other
    The concept of coloring a graph will lead to the definition of a complete n- coloring of a graph G which results the achromatic number ψ(G) where the maximum number of colors required for the points of G in which every pair of colors appears on at least one pair of adjacent vertices. In this paper, we obtain the achromatic number for the Central graph of Ladder graph, Central graph of Dutch-Windmill graph, Central graph of Fan graph and Central graph of Flower graph is denoted as ψ[C(L_{n})], ψ[C(D₃⁽ⁿ⁾)], ψ[C(F_{m,n})] and ψ[C(FL_{n})] respectively.
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    On b-coloring of central graph of some graphs
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Kalpana, M.; Vijayalakshmi, D.; Other; Other
    The b-chromatic number of G, denoted by ϕ(G), is the maximum k for which G has a b-coloring by k colors. A b-coloring of G by k colors is a proper k-coloring of the vertices of G such that in each color class i there exists a vertex x_{i} having neighbors in all the other k-1 color classes. Such a vertex x_{i} is called a b-dominating vertex, and the set of vertices {x₁,x₂…x_{k}} is called a b-dominating system. In this paper, we are going to investigate on the b-chromatic number of Central graph of Triangular Snake graph, Sunlet graph, Helm Graph, Double Triangular Snake graph, Gear graph, and Closed Helm graph are denoted as C(T_{n}), C(S_{n}), C(H_{n}), C(DT_{n}), C(G_{n}), C(CH_{n}) respectively.
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    Vertex magic total labeling of middle and total graph of cycle
    (Ankara Üniversitesi Fen Fakültesi, 2019-08-01) Kumar, Vimal; Vijayalakshmi, D.; Other; Other
    A vertex magic total labeling is a bijection from the union of the vertex set and edge set to the consecutive integers 1,2,3,....,v+e with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k, for some constant k. In this paper, we establish the vertex magic labeling of some classes of graphs and provide some open problems related to it.