Middle graph

Middle graph --- серединный граф.

The middle graph of a graph [math]\displaystyle{ G }[/math] is the graph obtained from [math]\displaystyle{ G }[/math] by inserting a new vertex into every edge of [math]\displaystyle{ G }[/math] and joining by edges those pairs of these new vertices which lie on adjacent edges of [math]\displaystyle{ G }[/math].

Let us denote the line graph of a graph [math]\displaystyle{ G }[/math] by [math]\displaystyle{ L(G) }[/math]. Then, from the definition of the endline graph and the middle graph of a graph [math]\displaystyle{ G }[/math], we have [math]\displaystyle{ L(G^{+}) = M(G) }[/math].