Browsing by Author "Godinho, Aloysius"

Now showing 1 - 9 of 9
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    Distance antimagic labeling of the ladder graph
    (2017-12) Godinho, Aloysius
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    Group Distance Magic Labeling of Crn
    (2017) Godinho, Aloysius
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    On nearly distance magic graphs
    (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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    Reconstruction of hypergraphs from line graphs and degree sequences
    (2020) Godinho, Aloysius
    In this paper we consider the problem to reconstruct a k-uniform hypergraph from its line graph. In general this problem is hard. We solve this problem when the number of hyperedges containing any pair of vertices is bounded. Given an integer sequence, constructing a k-uniform hypergraph with that as its degree sequence is NP-complete. Here we show that for constant integer sequences the question can be answered in polynomial time using Baranyai’s theorem.
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    Some distance antimagic labeled graphs
    (2016) Godinho, Aloysius
    Abstract. 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
    (2017-12) Godinho, Aloysius
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    Studies in Neighbourhood magic graphs
    (2021) Godinho, Aloysius
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    THE DISTANCE MAGIC INDEX OF A GRAPH
    (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