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Classifying Seven-Valent Symmetric Graphs of Order 8<i>pq</i>
oleh: Yingbi Jiang, Bo Ling, Jinlong Yang, Yun Zhao
Format: | Article |
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Diterbitkan: | MDPI AG 2024-03-01 |
Deskripsi
A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8</mn><mi>p</mi></mrow></semantics></math></inline-formula> for each prime <i>p</i>. We shall generalize this result by determining all of the connected seven-valent symmetric graphs of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8</mn><mi>p</mi><mi>q</mi></mrow></semantics></math></inline-formula> with <i>p</i> and <i>q</i> to be distinct primes. As a result, we show that for each such graph of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula>, it is isomorphic to one of seven graphs.