Department of Mathematics

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http://rcca.ndl.gov.in/handle/123456789/224

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Browsing Department of Mathematics by Author "Godinho, Aloysius"

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    Distance Antimagic Labeling of the Join & Corona Product of two Graphs
    (AKCE International Journal of Graphs and Combinatorics, 2017) Godinho, Aloysius
    Let G be a graph of order n. Let f∶ V (G)→{1, 2,..., n} be a bijection. The weight wf (v) of a vertex with respect to f is defined by wf (v)=∑ x∈ N (v) f (x). The labeling f is said to be distance antimagic if wf (u)≠ wf (v) for every pair of vertices u, v∈ V (G). If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we prove that Pm+ Pn, Pm+ Cn, Pm+ Wn and Cm+ Wn are distance antimagic. We have also proved that if G and H are distance antimagic graphs satisfying certain conditions, then G+ H is distance antimagic and if G is magic and H is arbirarily distance antimagic then G○ H is distance antimagic.
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    Distance antimagic labeling of the ladder graph
    (Electronic Notes in Discrete Mathematics 63 (2017) 317–322, 2017) Godinho, Aloysius
    Let G be a graph of order n. Let f : V (G) −→ {1, 2,...,n} be a bijection. The weight wf (v) of a vertex with respect to f is defined by wf (v) = x∈N(v) f(x). The labeling f is said to be distance antimagic if wf (u) = wf (v) for every pair of vertices u, v ∈ V (G). If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we investigate the existence of distance antimagic labeling in the ladder graph Ln ∼= P2Pn.
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    Group Distance Magic Labeling of Crn
    (Algorithms and Discrete Applied Mathematics, 2017) Godinho, Aloysius
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    On nearly distance magic graphs
    (International Conference, ICTCSDM 2016, Krishnankoil, India, December 19-21, 2016, 2017) Godinho, Aloysius
    Let G = (V, E) be a graph on n vertices. A bijection f ∶ V → {1, 2, . . . , n} is called a nearly distance magic labeling of G if there exist a positive integer k such that ∑x∈N(v) f(x) = k or k +1 for every v ∈ V . The constant k is called magic constants of the graph and the graph which admits such a labeling is called a nearly distance magic graph. In this paper we present several basic results on nearly distance magic graphs and compute the magic constant k in terms of the fractional total domination number of the graph.
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    Some distance antimagic labeled graphs
    (Algorithms and Discrete Applied Mathematics (pp. 190-200)., 2016-02) Godinho, Aloysius
    Let G be a graph of order n. A bijection f : V (G) −→ {1, 2, . . . , n} is said to be distance antimagic if for every vertex v the vertex weight defined by wf (v) = P x∈N(v) f(x) is distinct. The graph which admits such a labeling is called a distance antimagic graph. For a positive integer k, define fk : V (G) −→ {1 + k, 2 + k, . . . , n + k} by fk(x) = f(x) + k. If wfk (u) 6= wfk (v) for every pair of vertices u, v ∈ V , for any k ≥ 0 then f is said to be an arbitrarily distance antimagic labeling and the graph which admits such a labeling is said to be an arbitrarily distance antimagic graph. In this paper, we provide arbitrarily distance antimagic labelings for rPn, generalised Petersen graph P(n, k), n ≥ 5, Harary graph H4,n for n 6= 6 and also prove that join of these graphs is distance antimagic.
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    Some distance magic graphs
    (AKCE International Journal of Graphs and Combinatorics 15 (2018) 1–6, 2018) Godinho, Aloysius
    A graph G = (V, E), where |V| = n and |E| = m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set {1, 2, . . . , n} such that, ∑ v∈N(u) f (v) = k, for all u ∈ V, which is a constant and independent of u, where N(u) is the open neighborhood of the vertex u. The constant k is called the distance magic constant of the graph G and such a labeling f is called distance magic labeling of G. In this paper, we present new results on distance magic labeling of C r n and neighborhood expansion Dn(G) of a graph G.
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    THE DISTANCE MAGIC INDEX OF A GRAPH
    (Discussiones Mathematicae Graph Theory 38 (2018) 135–142, 2018) Godinho, Aloysius
    Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection φ : V (G) → S satisfying P x∈N(u) φ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeling. Then i(G) − n is called the distance magic index of the graph G. In this paper we determine the distance magic index of trees and complete bipartite graphs.