85 research outputs found

    Odd Harmonious Labeling of Some Graphs

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    The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling

    On the number of unlabeled vertices in edge-friendly labelings of graphs

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    Let GG be a graph with vertex set V(G)V(G) and edge set E(G)E(G), and ff be a 0-1 labeling of E(G)E(G) so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling ff \emph{edge-friendly}. We say an edge-friendly labeling induces a \emph{partial vertex labeling} if vertices which are incident to more edges labeled 1 than 0, are labeled 1, and vertices which are incident to more edges labeled 0 than 1, are labeled 0. Vertices that are incident to an equal number of edges of both labels we call \emph{unlabeled}. Call a procedure on a labeled graph a \emph{label switching algorithm} if it consists of pairwise switches of labels. Given an edge-friendly labeling of KnK_n, we show a label switching algorithm producing an edge-friendly relabeling of KnK_n such that all the vertices are labeled. We call such a labeling \textit{opinionated}.Comment: 7 pages, accepted to Discrete Mathematics, special issue dedicated to Combinatorics 201

    Hadamard matrices modulo 5

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    In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5-modular Hadamard matrices of order n if and only if n != 3, 7 (mod 10) or n != 6, 11. In particular, this solves the 5-modular version of the Hadamard conjecture.Comment: 7 pages, submitted to JC

    All trees are six-cordial

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    For any integer k>0k>0, a tree TT is kk-cordial if there exists a labeling of the vertices of TT by Zk\mathbb{Z}_k, inducing a labeling on the edges with edge-weights found by summing the labels on vertices incident to a given edge modulo kk so that each label appears on at most one more vertex than any other and each edge-weight appears on at most one more edge than any other. We prove that all trees are six-cordial by an adjustment of the test proposed by Hovey (1991) to show all trees are kk-cordial.Comment: 16 pages, 12 figure

    Some Classes of Cubic Harmonious Graphs

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    In this paper we proved some new theorems related with Cubic Harmonious Labeling. A (n,m) graph G =(V,E) is said to be Cubic Harmonious Graph(CHG) if there exists an injective function f:V(G)?{1,2,3,………m3+1} such that the induced mapping f *chg: E(G)? {13,23,33,……….m3} defined by f *chg (uv) = (f(u)+f(v)) mod (m3+1) is a bijection. In this paper, focus will be given on the result “cubic harmonious labeling of star, the subdivision of the edges of the star K1,n , the subdivision of the central edge of the bistar Bm,n, Pm ? nK1”

    (Di)graph products, labelings and related results

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    Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can also obtain enumerative results that provide lower bounds on the number of nonisomorphic labelings of a particular type. In this paper, we will focus in three of the (di)graphs products that have been used in these duties: the ⊗h-product of digraphs, the weak tensor product of graphs and the weak ⊗h-product of graphs.Reseach supported by the Spanish Government under project MTM2014-60127-P and symbolically by the Catalan Research Council under grant 2014SGR1147
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