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- W1977294862 abstract "An adjacent vertex-distinguishing edge coloring of a simple graph G is a proper edge coloring of G such that incident edge sets of any two adjacent vertices are assigned different sets of colors. A total coloring of a graph G is a coloring of both the edges and the vertices. A total coloring is proper if no two adjacent or incident elements receive the same color. An adjacent vertex-distinguishing total coloring h of a simple graph G=(V,E) is a proper total coloring of G such that H(u)≠H(v) for any two adjacent vertices u and v, where H(u)={h(wu)|wu∈E(G)}∪{h(u)} and H(v)={h(xv)|xv∈E(G)}∪{h(v)}. The minimum number of colors required for an adjacent vertex-distinguishing edge coloring (resp. an adjacent vertex-distinguishing total coloring) of G is called the adjacent vertex-distinguishing edge chromatic number (resp. adjacent vertex-distinguishing total chromatic number) of G and denoted by χav′(G) (resp. χat(G)). In this paper, we consider the adjacent vertex-distinguishing edge chromatic number and adjacent vertex-distinguishing total chromatic number of the hypercube Qn, prove that χav′(Qn)=Δ(Qn)+1 for n⩾3 and χat(Qn)=Δ(Qn)+2 for n⩾2." @default.
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- W1977294862 date "2009-05-01" @default.
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- W1977294862 title "Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes" @default.
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- W1977294862 doi "https://doi.org/10.1016/j.ipl.2009.02.006" @default.
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