| 摘要: |
| 有限群的广义素互素图，以群的非单位元为顶点集，两点相邻当且仅当其阶的最大公因数为 1 或素数. 本文给出了广义素互素图为欧拉图的充要条件，研究了特定有限群上广义素互素图的哈密顿性与顶点连通度，以及其拉谱拉斯谱和无符号拉谱拉斯谱. |
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Li Junhao, Huo Lijun
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| Abstract: |
| The generalized prime-coprime graph of a finite group takes all non-identity elements of the group as its vertex set，and two distinct vertices are adjacent if and only if the greatest common divisor of their orders is 1 or a prime number. This paper presents a necessary and sufficient condition for the generalized prime-coprime graph to be Eulerian, and investigates the Hamiltonicity，vertex-connectivity, Laplacian spectra and signless Laplacian spectra of the generalized prime-coprime graph on specific finite groups. |
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