Connectivity of intersection graphs of finite groups |
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Authors: | Selçuk Kayacan |
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Affiliation: | Department of Mathematics, Istanbul Technical University, Maslak, Istanbul, Turkey |
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Abstract: | The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper, we classify finite solvable groups whose intersection graphs are not 2-connected and finite nilpotent groups whose intersection graphs are not 3-connected. Our methods are elementary. |
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Keywords: | Connectivity finite groups intersection graph subgroup |
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