arXiv subjects
Publications and source records attributed to M S Sunitha.
For a finite group $G$ the co-prime graph $\Gamma(G)$ is defined as a graph with vertex set $G$ in which two distinct vertices $x$ and $y$ are adjacent if and only if $gcd(o(x),o(y))=1$ where $o(x)$ and $o(y)$ denote the orders of the elements $x$ and $y$ respectively. In this paper we find properties of groups whose co-prime graphs forbid graphs such as $C_4,K_{1,3},P_4$ and asteroidal triples.
For a finite group $G$ and for a fixed positive integer $k$, $k\geq 2$, the $k$-power graph of $G$ is an undirected simple graph with vertex set $G$ in which two distinct vertices $x$ and $y$ are adjacent if and only if $x^k=y$ or $y^k=x$. In this paper, we investigate some graph parameters such as number of edges, clique number, connectedness, etc. of $k$-power graphs of finite groups. Also find some properties of $k$-power graphs of finite cyclic groups, and finally we present an application
The power graph $P(G)$ of a finite group $G$ is the undirected simple graph with vertex set $G$, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph $P_e(G)$ of $G$ (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of $G$.