Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is familiar to us by the name of “total coloring”. Total coloring is a coloring of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$V\cup {E}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>V</mi> <mo>∪</mo> <mi>E</mi> </mrow> </math> </EquationSource> </InlineEquation> such that no two adjacent or incident elements receive the same color. In other words, total chromatic number of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> is the minimum number of disjoint vertex independent sets covering a total graph of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation>. Here, let <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> be a planar graph with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\varDelta \ge 8$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">Δ</mi> <mo>≥</mo> <mn>8</mn> </mrow> </math> </EquationSource> </InlineEquation>. We proved that if for every vertex <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$v\in V$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>v</mi> <mo>∈</mo> <mi>V</mi> </mrow> </math> </EquationSource> </InlineEquation>, there exists two integers <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$i_{v},j_{v} \in \{3,4,5,6,7,8\}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>i</mi> <mi>v</mi> </msub> <mo>,</mo> <msub> <mi>j</mi> <mi>v</mi> </msub> <mo>∈</mo> <mrow> <mo stretchy="false">{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mn>8</mn> <mo stretchy="false">}</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> such that <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$v$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>v</mi> </math> </EquationSource> </InlineEquation> is not incident with intersecting <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$$i_v$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>i</mi> <mi>v</mi> </msub> </math> </EquationSource> </InlineEquation>-cycles and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$$j_v$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>j</mi> <mi>v</mi> </msub> </math> </EquationSource> </InlineEquation>-cycles, then the vertex chromatic number of total graph of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> is <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$$\varDelta +1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">Δ</mi> <mo>+</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, i.e., the total chromatic number of <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation> is <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$$\varDelta +1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">Δ</mi> <mo>+</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. Copyright Springer Science+Business Media New York 2014