Group of tabulars under one table reference

I suggest you load the subcaption package, which provides an environment called subtable. To (more or less) replicate the structure shown in the screenshot you posted, you could set up three subtable environments, each with its own \caption, inside the overall table environment. In the code below, each subtable contains two tabular environments.

\documentclass{article} % or some other, more suitable document class
\usepackage{array} % for '\extrarowheight' macro
\usepackage{subcaption} % for 'subtable' environment
\begin{document}

\begin{table}[!htb]
\setlength{\extrarowheight}{1pt} % for a more open "look"

\centering

\begin{subtable}{.55\linewidth} % choose width suitably
\begin{tabular}{|c|c|} % 1st tabular
\multicolumn{2}{c}{$G$}\\
\hline
Vertex & Label\\ 
\hline
b & 1 \\
c & 1 \\
d & 1 \\ \hline
\end{tabular}%
\hfill % maximize distance between adjacent tabulars
\begin{tabular}{|c|c|} % 2nd tabular
\multicolumn{2}{c}{$H$}\\
\hline
Vertex & Label\\ 
\hline
c & 1 \\
a & 1 \\
d & 1 \\ \hline
\end{tabular}

\smallskip
\caption{$M=\{a,b\}$}
\end{subtable}

\vspace{5mm} % insert a bit of vertical whitespace
\begin{subtable}{.55\linewidth}
\begin{tabular}{|c|c|}
\multicolumn{2}{c}{$G$}\\
\hline
Vertex & Label\\ 
\hline
c & 11 \\
d & 10 \\ \hline
\end{tabular}%
\hfill
\begin{tabular}{|c|c|}
\multicolumn{2}{c}{$H$}\\
\hline
Vertex & Label\\ 
\hline
a & 11 \\
d & 11 \\ \hline
\end{tabular}

\smallskip
\caption{$M=\{ab,bc\}$}
\end{subtable}

\vspace{5mm}
\begin{subtable}{.55\linewidth}
\begin{tabular}{|c|c|}
\multicolumn{2}{c}{$G$}\\
\hline
Vertex & Label\\ 
\hline
d & 101 \\ \hline
\end{tabular}%
\hfill
\begin{tabular}{|c|c|}
\multicolumn{2}{c}{$H$}\\
\hline
Vertex & Label\\ 
\hline
d & 110 \\ \hline
\end{tabular}

\smallskip
\caption{$M=\{abc,bca\}$}
\end{subtable}

\caption{Labels on the non-mapped vertices of $G$ and $H$, for selected choices of mapping $M$}
\end{table}
\end{document}

It is also possible to build these tabulars using cals and one calstable. By defining shortcuts for removing cell border, it is convinient to remove the necessary borders around the cells. Of cause, sub-labels are ordinary text, so it is not possible to refer to subtable 1(c). If you prefer more narrow table, just increase the the divisor when calculating the column width.

\documentclass{article}
\usepackage{cals, caption}

\let\nc=\nullcell                        % Shortcuts
\let\sc=\spancontent

\begin{document}

\begin{table}[ht]

\begin{calstable}[c] % Centre the tabular

% Defining columns relative to the margin 
\colwidths{{\dimexpr(\columnwidth)/5\relax}  % Increase 5 to 6 or 7 to make the tabular more narrow 
            {\dimexpr(\columnwidth)/5\relax}
            {\dimexpr(\columnwidth)/5\relax}
            {\dimexpr(\columnwidth)/5\relax}
            {\dimexpr(\columnwidth)/5\relax}
            }

% Set up the tabular
\makeatletter
\def\cals@framers@width{0.4pt}   % Outside frame rules, reduce if the rule is too heavy
\def\cals@framecs@width{0.4pt}
\def\cals@bodyrs@width{0.4pt}
\def\cals@cs@width{0.4pt}             % Inside rules, reduce if the rule is too heavy
\def\cals@rs@width{0.4pt}

\def\tb{\ifx\cals@borderT\relax     % Top border switch (off-on)
    \def\cals@borderT{0pt}
\else \let\cals@borderT\relax\fi}

\def\bb{\ifx\cals@borderB\relax     % Botton border switch (off-on)
    \def\cals@borderB{0pt}
\else \let\cals@borderB\relax\fi}

\def\rb{\ifx\cals@borderR\relax     % Right border switch (off-on)
    \def\cals@borderR{0pt}
\else \let\cals@borderR\relax\fi}

\def\lb{\ifx\cals@borderL\relax     % Left border switch (off-on)
    \def\cals@borderL{0pt}
\else \let\cals@borderL\relax\fi}


% R1H1
\brow
    \lb\tb\rb\alignC\nc{ltb}
    \nc{rtb}\sc{$G$}
    \bb\cell{}\bb
    \nc{ltb}
    \nc{rtb}\sc{$H$}\lb\tb\rb
\erow
% R2B1
\brow
    \cell{Vertex}
    \cell{Label}
    \bb\cell{}\bb
    \cell{Vertex}
    \cell{Label}
\erow
% R3B2
\brow
    \cell{b}
    \cell{1}
    \bb\cell{}\bb
    \cell{c}
    \cell{1}
\erow
% R4B3
\brow
    \cell{c}
    \cell{1}
    \bb\cell{}\bb
    \cell{a}
    \cell{1}
\erow
% R5B4
\brow
    \cell{d}
    \cell{1}
    \bb\cell{}\bb
    \cell{d}
    \cell{1}
\erow
% R6B5
\brow
    \lb\rb\nc{ltb}
    \nc{tb}
    \nc{tb}
    \nc{tb}
    \nc{rtb}\sc{(a)}\lb\rb
\erow
% R7B6
\brow
    \lb\tb\rb\alignC\nc{ltb}
    \nc{rtb}\sc{$G$}
    \bb\cell{}\bb
    \nc{ltb}
    \nc{rtb}\sc{$H$}\lb\tb\rb
\erow
% R8B7
\brow
    \cell{Vertex}
    \cell{Label}
    \bb\cell{}\bb
    \cell{Vertex}
    \cell{Label}
\erow
% R9B8
\brow
    \cell{c}
    \cell{11}
    \bb\cell{}\bb
    \cell{a}
    \cell{11}
\erow
% R10B9
\brow
    \cell{d}
    \cell{10}
    \bb\cell{}\bb
    \cell{d}
    \cell{11}
\erow
% R11B10
\brow
    \rb\lb\nc{ltb}
    \nc{tb}
    \nc{tb}
    \nc{tb}
    \nc{rtb}\sc{(b)}\rb\lb
\erow
% R12B11
\brow
    \lb\tb\rb\alignC\nc{ltb}
    \nc{rtb}\sc{$G$}
    \bb\cell{}\bb
    \nc{ltb}
    \nc{rtb}\sc{$H$}\lb\tb\rb
\erow
% R13B12
\brow
    \cell{Vertex}
    \cell{Label}
    \bb\cell{}\bb
    \cell{Vertex}
    \cell{Label}
\erow
% R14B13
\brow
    \cell{d}
    \cell{101}
    \bb\cell{}\bb
    \cell{d}
    \cell{101}
\erow
% R15B14
\brow
    \lb\rb\bb\nc{ltb}
    \nc{tb}
    \nc{tb}
    \nc{tb}
    \nc{rtb}\sc{(c)}\lb\rb\bb
\erow
\makeatletter
\end{calstable}\par % \par to align the tabular

\caption{Labels on the non-mapped vertices of $G$ and $H$ with mapping: Fig (a) $M={a,b}$, Fig. (b) $M={ab,bc}$, and (c) $M={abc, bca}$}
\end{table}

\end{document}