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I'm trying to reproduce a structure like this:

But all I could come up with was the following code:

begintable[!htb]
 captionGlobal caption
 beginminipage.5linewidth
 caption*$G$
 centering
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage%
 beginminipage.5linewidth
 centering
 caption*$F$
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage 
endtable

begintable[!htb]
 caption*Global caption
 beginminipage.5linewidth
 caption*$G$
 centering
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage%
 beginminipage.5linewidth
 centering
 caption*$F$
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage 
endtable

begintable[!htb]
 caption*Global caption
 beginminipage.5linewidth
 caption*$G$
 centering
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage%
 beginminipage.5linewidth
 centering
 caption*$F$
 begintabularc
 cline1-2
 textbfVertex & textbfLabel\ cline1-2
 b & 1 \
 c & 1 \
 d & 1 \ cline1-2
 endtabular
 endminipage 
endtable

which somewhat resembles the structure, but keeps my tables way too much separated from each other. Can anyone suggest me a better way to obtain the desired results?

Thank you in advance.

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.

documentclassarticle
usepackagecals, caption

letnc=nullcell % Shortcuts
letsc=spancontent

begindocument

begintable[ht]

begincalstable[c] % Centre the tabular

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

% Set up the tabular
makeatletter
defcals@framers@width0.4pt % Outside frame rules, reduce if the rule is too heavy
defcals@framecs@width0.4pt
defcals@bodyrs@width0.4pt
defcals@cs@width0.4pt % Inside rules, reduce if the rule is too heavy
defcals@rs@width0.4pt

deftbifxcals@borderTrelax % Top border switch (off-on)
 defcals@borderT0pt
else letcals@borderTrelaxfi

defbbifxcals@borderBrelax % Botton border switch (off-on)
 defcals@borderB0pt
else letcals@borderBrelaxfi

defrbifxcals@borderRrelax % Right border switch (off-on)
 defcals@borderR0pt
else letcals@borderRrelaxfi

deflbifxcals@borderLrelax % Left border switch (off-on)
 defcals@borderL0pt
else letcals@borderLrelaxfi


% R1H1
brow
 lbtbrbalignCncltb
 ncrtbsc$G$
 bbcellbb
 ncltb
 ncrtbsc$H$lbtbrb
erow
% R2B1
brow
 cellVertex
 cellLabel
 bbcellbb
 cellVertex
 cellLabel
erow
% R3B2
brow
 cellb
 cell1
 bbcellbb
 cellc
 cell1
erow
% R4B3
brow
 cellc
 cell1
 bbcellbb
 cella
 cell1
erow
% R5B4
brow
 celld
 cell1
 bbcellbb
 celld
 cell1
erow
% R6B5
brow
 lbrbncltb
 nctb
 nctb
 nctb
 ncrtbsc(a)lbrb
erow
% R7B6
brow
 lbtbrbalignCncltb
 ncrtbsc$G$
 bbcellbb
 ncltb
 ncrtbsc$H$lbtbrb
erow
% R8B7
brow
 cellVertex
 cellLabel
 bbcellbb
 cellVertex
 cellLabel
erow
% R9B8
brow
 cellc
 cell11
 bbcellbb
 cella
 cell11
erow
% R10B9
brow
 celld
 cell10
 bbcellbb
 celld
 cell11
erow
% R11B10
brow
 rblbncltb
 nctb
 nctb
 nctb
 ncrtbsc(b)rblb
erow
% R12B11
brow
 lbtbrbalignCncltb
 ncrtbsc$G$
 bbcellbb
 ncltb
 ncrtbsc$H$lbtbrb
erow
% R13B12
brow
 cellVertex
 cellLabel
 bbcellbb
 cellVertex
 cellLabel
erow
% R14B13
brow
 celld
 cell101
 bbcellbb
 celld
 cell101
erow
% R15B14
brow
 lbrbbbncltb
 nctb
 nctb
 nctb
 ncrtbsc(c)lbrbbb
erow
makeatletter
endcalstablepar % par to align the tabular

captionLabels on the non-mapped vertices of $G$ and $H$ with mapping: Fig (a) $M=a,b$, Fig. (b) $M=ab,bc$, and (c) $M=abc, bca$
endtable

enddocument

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.

documentclassarticle % or some other, more suitable document class
usepackagearray % for 'extrarowheight' macro
usepackagesubcaption % for 'subtable' environment
begindocument

begintable[!htb]
setlengthextrarowheight1pt % for a more open "look"

centering

beginsubtable.55linewidth % choose width suitably
begintabular % 1st tabular
multicolumn2c$G$\
hline
Vertex & Label\ 
hline
b & 1 \
c & 1 \
d & 1 \ hline
endtabular%
hfill % maximize distance between adjacent tabulars
begintabular % 2nd tabular
multicolumn2c$H$\
hline
Vertex & Label\ 
hline
c & 1 \
a & 1 \
d & 1 \ hline
endtabular

smallskip
caption$M=a,b$
endsubtable

vspace5mm % insert a bit of vertical whitespace
beginsubtable.55linewidth
begintabular
multicolumn2c$G$\
hline
Vertex & Label\ 
hline
c & 11 \
d & 10 \ hline
endtabular%
hfill
begintabular
multicolumn2c$H$\
hline
Vertex & Label\ 
hline
a & 11 \
d & 11 \ hline
endtabular

smallskip
caption$M=ab,bc$
endsubtable

vspace5mm
beginsubtable.55linewidth
begintabular
multicolumn2c$G$\
hline
Vertex & Label\ 
hline
d & 101 \ hline
endtabular%
hfill
begintabular
multicolumn2c$H$\
hline
Vertex & Label\ 
hline
d & 110 \ hline
endtabular

smallskip
caption$M=abc,bca$
endsubtable

captionLabels on the non-mapped vertices of $G$ and $H$, for selected choices of mapping $M$
endtable
enddocument