3,940 research outputs found
Orientable β€ \u3c inf\u3e n -distance magic labeling of the Cartesian product of many cycles
The following generalization of distance magic graphs was introduced in [2]. A directed β€n- distance magic labeling of an oriented graph G = (V,A) of order n is a bijection β: V β β€n with the property that there is a ΞΌ β β€n (called the magic constant) such that If for a graph G there exists an orientation G such that there is a directed β€n-distance magic labeling β for G, we say that G is orientable β€n-distance magic and the directed β€n-distance magic labeling β we call an orientable β€n-distance magic labeling. In this paper, we find orientable β€n- distance magic labelings of the Cartesian product of cycles. In addition, we show that even-ordered hypercubes are orientable β€n-distance magic
Orientable Z_n-distance Magic Labeling of the Cartesian Product of Many Cycles
The following generalization of distance magic graphs was introduced in [2]. A directed Z_n-distance magic labeling of an oriented graph of order n is a bijection with the property that there is a (called the magic constant) such that w(x)= \sum_{y\in N_{G}^{+}(x)} \overrightarrow{\ell}(y) - \sum_{y\in N_{G}^{-}(x)} \overrightarrow{\ell}(y)= \mu\overrightarrow{G}\overrightarrow{\ell}\overrightarrow{G}\overrightarrow{\ell}$ we call an orientable Z_n-distance magic labeling. In this paper, we find orientable Z_n-distance magic labelings of the Cartesian product of cycles. In addition, we show that even-ordered hypercubes are orientable Z_n-distance magic
On Distance Magic Harary Graphs
This paper establishes two techniques to construct larger distance magic and
(a, d)-distance antimagic graphs using Harary graphs and provides a solution to
the existence of distance magicness of legicographic product and direct product
of G with C4, for every non-regular distance magic graph G with maximum degree
|V(G)|-1.Comment: 12 pages, 1 figur
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