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Difference cordiality of product related graphs. (English) Zbl 1311.05171

Summary: Let \(G\) be a \((p, q)\) graph. Let \(f : V (G) \to \{1, 2, \ldots, p\}\) be a function. For each edge \(uv\), assign the label \(|f(u) - f(v)|\). \(f\) is called a difference cordial labeling if \(f\) is an injective map and \(|e_f (0) - e_{f} (1)| \leq 1\) where \(e_{f} (1)\) and \(e_{f} (0)\) denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph which admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordiality of torus grids \(C_{m} \times C_{n}, K_{m} \times P_{2}\), prism, book, Möbius ladder, Mongolian tent and \(n\)-cube.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C76 Graph operations (line graphs, products, etc.)
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