\documentclass[tikz,border=5pt]{standalone}
\usepackage{amsmath,amssymb,tikz}
\begin{document}
\begin{tikzpicture}[scale=.85, thick, x=0.85cm, y=0.85cm]
\def\vr{2.25pt}
\path (0,0) coordinate (u1);
\path (0,1) coordinate (v1);
\path (1,0) coordinate (u2);
\path (1,1) coordinate (v2);
\path (2,0) coordinate (u3);
\path (2,1) coordinate (v3);
\path (3,0) coordinate (u4);
\path (3,1) coordinate (v4);
\path (5,0) coordinate (u5);
\path (5,1) coordinate (v5);
\path (2.5,2) coordinate (v);
\draw (v)--(v1)--(u1);
\draw (v)--(v2)--(u2);
\draw (v)--(v3)--(u3);
\draw (v)--(v4)--(u4);
\draw (v)--(v5)--(u5);
\draw (v1)--(v2);
\draw[fill=black] (v1) circle (\vr);
\draw[fill=black] (v2) circle (\vr);
\draw[fill=black] (v3) circle (\vr);
\draw[fill=black] (v4) circle (\vr);
\draw[fill=black] (v5) circle (\vr);
\draw[fill=white] (u1) circle (\vr);
\draw[fill=white] (u2) circle (\vr);
\draw[fill=black] (u3) circle (\vr);
\draw[fill=black] (u4) circle (\vr);
\draw[fill=black] (u5) circle (\vr);
\draw[fill=black] (v) circle (\vr);
\draw (2.5,-2.5) node {\small (a) $G_1$};
\draw (4,1) node {$\cdots$};
\draw (4,0) node {$\cdots$};
\draw (2.5,-0.5) node {$\underbrace{\phantom{1111111111111111111}}$};
\draw (2.5,-1.2) node {$2 \le k \le \Delta$};
\draw (0.5,0.7) node {$e$};
\path (7,0) coordinate (u1);
\path (7,1) coordinate (v1);
\path (8,0) coordinate (u2);
\path (8,1) coordinate (v2);
\path (9,0) coordinate (u3);
\path (9,1) coordinate (v3);
\path (10,0) coordinate (u4);
\path (10,1) coordinate (v4);
\path (12,0) coordinate (u5);
\path (12,1) coordinate (v5);
\path (9.5,2) coordinate (v);
\draw (v)--(v1)--(u1);
\draw (v)--(v2)--(u2);
\draw (v)--(v3)--(u3);
\draw (v)--(v4)--(u4);
\draw (v)--(v5)--(u5);
\draw (u1)--(u2);
\draw[fill=white] (v1) circle (\vr);
\draw[fill=black] (v2) circle (\vr);
\draw[fill=black] (v3) circle (\vr);
\draw[fill=black] (v4) circle (\vr);
\draw[fill=black] (v5) circle (\vr);
\draw[fill=white] (u1) circle (\vr);
\draw[fill=black] (u2) circle (\vr);
\draw[fill=black] (u3) circle (\vr);
\draw[fill=black] (u4) circle (\vr);
\draw[fill=black] (u5) circle (\vr);
\draw[fill=black] (v) circle (\vr);
\draw (9.5,-2.5) node {\small (b) $G_2$};
\draw (11,1) node {$\cdots$};
\draw (11,0) node {$\cdots$};
\draw (9.5,-0.5) node {$\underbrace{\phantom{1111111111111111111}}$};
\draw (9.5,-1.2) node {$2 \le k \le \Delta$};
\draw (7.5,0.3) node {$e$};
\path (14,0) coordinate (u1);
\path (14,1) coordinate (v1);
\path (15,0) coordinate (u2);
\path (15,1) coordinate (v2);
\path (16,0) coordinate (u3);
\path (16,1) coordinate (v3);
\path (17,0) coordinate (u4);
\path (17,1) coordinate (v4);
\path (19,0) coordinate (u5);
\path (19,1) coordinate (v5);
\path (16.5,2) coordinate (v);
\draw (v)--(v1)--(u1);
\draw (v)--(v2)--(u2);
\draw (v)--(v3)--(u3);
\draw (v)--(v4)--(u4);
\draw (v)--(v5)--(u5);
\draw (v) to[out=0,in=40, distance=2cm] (u5);
\draw[fill=black] (v1) circle (\vr);
\draw[fill=black] (v2) circle (\vr);
\draw[fill=black] (v3) circle (\vr);
\draw[fill=black] (v4) circle (\vr);
\draw[fill=black] (v5) circle (\vr);
\draw[fill=white] (u1) circle (\vr);
\draw[fill=black] (u2) circle (\vr);
\draw[fill=black] (u3) circle (\vr);
\draw[fill=black] (u4) circle (\vr);
\draw[fill=black] (u5) circle (\vr);
\draw[fill=black] (v) circle (\vr);
\draw (16.5,-2.5) node {\small (c) $G_3$};
\draw (18,1) node {$\cdots$};
\draw (18,0) node {$\cdots$};
\draw (16.5,-0.5) node {$\underbrace{\phantom{1111111111111111111}}$};
\draw (16.5,-1.2) node {$2 \le k \le \Delta - 1$};
\draw (19.9,1.5) node {$e$};
\end{tikzpicture}
\end{document}