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Vertex-distinguishing I-total colorings and vertex-distinguishing VI-total colorings of graph \(m{C_8}\). (Chinese. English summary) Zbl 1488.05209

Summary: By constructing a matrix which was composed of color sets and empty set as the elements, using the distributing method of color sets in advance and specific coloring scheme, we gave the best vertex-distinguishing I-total colorings (VDITC) and the best vertex-distinguishing VI-total colorings (VDVITC) of graph \(m{C_8}\). Thus vertex-distinguishing I-total chromatic numbers and the vertex-distinguishing VI-total chromatic numbers of graph \(m{C_8}\) were determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph \(m{C_8}\).

MSC:

05C15 Coloring of graphs and hypergraphs
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