| Summary: | Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></semantics></math></inline-formula> be a connected graph with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi>V</mi><mo>|</mo><mo>=</mo><mi>n</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi>E</mi><mo>|</mo><mo>=</mo><mi>m</mi></mrow></semantics></math></inline-formula>. A bijection <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>∪</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>}</mo></mrow></semantics></math></inline-formula> is called local antimagic total labeling if, for any two adjacent vertices <i>u</i> and <i>v</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>t</mi></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≠</mo><msub><mi>ω</mi><mi>t</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>t</mi></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><msub><mo>∑</mo><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></msub><mi>f</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula> is the set of edges incident to <i>u</i>. Thus, any local antimagic total labeling induces a proper coloring of <i>G</i>, where the vertex <i>x</i> in <i>G</i> is assigned the color <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>t</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The local antimagic total chromatic number, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>χ</mi><mrow><mi>l</mi><mi>a</mi><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, is the minimum number of colors taken over all colorings induced by local antimagic total labelings of <i>G</i>. In this paper, we present the local antimagic total chromatic numbers of some wheel-related graphs, such as the fan graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mi>n</mi></msub></semantics></math></inline-formula>, the bowknot graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>B</mi><mrow><mi>n</mi><mo>,</mo><mi>n</mi></mrow></msub></semantics></math></inline-formula>, the Dutch windmill graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>D</mi><mrow><mn>4</mn></mrow><mi>n</mi></msubsup></semantics></math></inline-formula>, the analogous Dutch graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><msubsup><mi>D</mi><mrow><mn>4</mn></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula> and the flower graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">F</mi><mi>n</mi></msub></semantics></math></inline-formula>.
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