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On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups | | Ramesh Prasad Panda
; K. V. Krishna
; | | Date: |
11 May 2017 | | Abstract: | The power graph of a group $G$ is the graph whose vertex set is $G$ and two
distinct vertices are adjacent if one is a power of the other. In this paper,
the minimum degree of power graphs of certain classes of cyclic groups, abelian
$p$-groups, dihedral groups and dicyclic groups are obtained. It is ascertained
that the edge-connectivity and minimum degree of power graphs are equal, and
consequently the minimum disconnecting sets of power graphs of the
aforementioned groups are determined. Then the equality of connectivity and
minimum degree of power graphs of finite groups is investigated and in this
connection, certain necessary conditions are produced. A necessary and
sufficient condition for the equality of connectivity and minimum degree of
power graphs of finite cyclic groups is obtained. Moreover, the equality is
examined for the power graphs of abelian $p$-groups, dihedral groups and
dicyclic groups. | | Source: | arXiv, 1705.4122 | | Services: | Forum | Review | PDF | Favorites | |
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