Non-Separating Planar Graphs

A graph $G$ is a non-separating planar if there drawing $D$ of on the plane such that (1) no two edges cross each other in and (2) for any cycle $C$ $D$, vertices not are same side $D$.
 Non-separating graphs closed under taking minors subclass superclass outerplanar graphs.
 In this paper, we show only it does contain $K_1 \cup K_4$ or K_{2,3}$ $K_{1,1,3}$ as minor.
 Furthermore, provide structural characterisation class graphs. More specifically, maximal either an wheel obtained from disjoint union triangles by adding three vertex-disjoint paths between triangles.
 Lastly, to demonstrate application graphs, use prove linkless with $3n-3$ edges. Thus, can have significantly fewer than maximum graphs; Sachs exhibited $n$ $4n-10$ (the possible) 1983.