85 research outputs found
Odd Harmonious Labeling of Some Graphs
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
Let be a graph with vertex set and edge set , and be a
0-1 labeling of so that the absolute difference in the number of edges
labeled 1 and 0 is no more than one. Call such a labeling
\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 , we show a label switching algorithm
producing an edge-friendly relabeling of 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
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
For any integer , a tree is -cordial if there exists a labeling
of the vertices of by , inducing a labeling on the edges with
edge-weights found by summing the labels on vertices incident to a given edge
modulo 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 -cordial.Comment: 16 pages, 12 figure
Some Classes of Cubic Harmonious Graphs
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
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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