On the independence number of the power graph of a finite group |
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Authors: | Xuanlong Ma Ruiqin Fu Xuefei Lu |
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Institution: | School of Science, Xi’an Shiyou University, Xi’an 710065, China |
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Abstract: | The power graph of a finite group is the graph whose vertex set is , two distinct elements being adjacent if one is a power of the other. In this paper, we give sharp lower and upper bounds for the independence number of and characterize the groups achieving the bounds. Moreover, we determine the independence number of if is cyclic, dihedral or generalized quaternion. Finally, we classify all finite groups whose power graphs have independence number 3 or , where is the order of . |
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Keywords: | Power graph Finite group Independence number |
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