Browsing by Author "Godinho, Aloysius"
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Item Distance antimagic labeling of join and corona of two graphs(/ AKCE International Journal of Graphs and Combinatorics 14 (2017) 172–177, 2017) Godinho, AloysiusItem Distance Antimagic Labeling of the Join & Corona Product of two Graphs(AKCE International Journal of Graphs and Combinatorics, 2017) Godinho, AloysiusLet 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.Item Distance antimagic labeling of the ladder graph(Electronic Notes in Discrete Mathematics 63 (2017) 317–322, 2017) Godinho, AloysiusLet 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.Item Group Distance Magic Labeling of Crn(Algorithms and Discrete Applied Mathematics, 2017) Godinho, AloysiusItem On local distance antimagic labeling of graphs(AKCE International Journal of Graphs and Combinatorics, 2023) Godinho, AloysiusLet G = (V, E) be a graph of order n and let f : V → {1, 2 ... , n} be a bijection. For every vertex v ∈ V, we define the weight of the vertex v as w(v) = x∈N(v) f(x) where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if w(u) = w(v)for every pair of adjacent vertices u, v ∈ V. The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number χld(G) to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn, the cycle Cn, the wheel graph Wn, friendship graph Fn, the corona product of graphs G ◦ Km, complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.Item On nearly distance magic graphs(International Conference, ICTCSDM 2016, Krishnankoil, India, December 19-21, 2016, 2017) Godinho, AloysiusLet 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.Item Reconstruction of hypergraphs from line graphs and degree sequences(arXiv:2104.14863v1, 2021) Godinho, AloysiusIn 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.Item Some distance antimagic labeled graphs(Algorithms and Discrete Applied Mathematics (pp. 190-200)., 2016-02) Godinho, AloysiusLet 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.Item Some distance magic graphs(AKCE International Journal of Graphs and Combinatorics 15 (2018) 1–6, 2018) Godinho, AloysiusA 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.Item Studies in Neighbourhood magic graphs(2021) Godinho, AloysiusItem THE DISTANCE MAGIC INDEX OF A GRAPH(Discussiones Mathematicae Graph Theory 38 (2018) 135–142, 2018) Godinho, AloysiusLet 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.