AVD proper edge-coloring of some families of graphs. (English) Zbl 1500.05019
Summary: Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of \(G\) in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edge-coloring of \(G\) is called the adjacent vertex-distinguishing proper edge-chromatic index. Adjacent vertex-distinguishing proper edge-chromatic indices of the middle graph, splitting graph and shadow graph of path and cycle are determined. Adjacent vertex-distinguishing proper edge-chromatic indices of the triangular grid \(T_n, H\)-graph and generalized \(H\)-graph are also determined.
MSC:
| 05C15 | Coloring of graphs and hypergraphs |
Keywords:
edge-coloring; AVD proper edge-coloring; path; cycle; middle graph; splitting graph; shadow graph; triangular grid \(T_n\); \(H\)-graphReferences:
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