The total chromatic number of a graph G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document}, denoted by χ′′(G)\documentclass[12pt]{minimal}
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\begin{document}$$\chi ''(G)$$\end{document}, is the minimum number of colors needed to color the vertices and edges of G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} such that no two adjacent or incident elements get the same color. It is known that if a planar graph G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} has maximum degree Δ(G)≥9\documentclass[12pt]{minimal}
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\begin{document}$$\Delta (G)\ge 9$$\end{document}, then χ′′(G)=Δ(G)+1\documentclass[12pt]{minimal}
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\begin{document}$$\chi ''(G)=\Delta (G)+1$$\end{document}. In this paper, it is proved that if G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is a planar graph with Δ(G)≥7\documentclass[12pt]{minimal}
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\begin{document}$$\Delta (G)\ge 7$$\end{document}, and for each vertex v\documentclass[12pt]{minimal}
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\begin{document}$$v$$\end{document}, there is an integer kv∈{3,4,5,6,7,8}\documentclass[12pt]{minimal}
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\begin{document}$$k_v\in \{3,4,5,6,7,8\}$$\end{document} such that there is no kv\documentclass[12pt]{minimal}
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\begin{document}$$k_v$$\end{document}-cycle which contains v\documentclass[12pt]{minimal}
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\begin{document}$$v$$\end{document}, then χ′′(G)=Δ(G)+1\documentclass[12pt]{minimal}
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\begin{document}$$\chi ''(G)=\Delta (G)+1$$\end{document}.
