Dgdrxrt

Is there a way to draw a dashed pattern between two nodes taking the middle point of these two nodes as the center point?

This is my code:

documentclassarticle
usepackage[utf8]inputenc
usepackageamsthm,amsmath,amssymb,authblk,tikz,graphicx
usetikzlibraryshapes,decorations,circuits.logic.US,circuits.logic.IEC,fit,external
tikzstyleloosely dashed=[dash pattern=on 4pt off 8pt]
tikzstyleloosely dashed2=[dash pattern=on 4pt off 8pt]

begindocument

beginfigure
 centering
 begintikzpicture[every node/.style = draw=none, text=black, circle, minimum size = 13mm, fill=gray!25]
 path
 (0,3) node(y) $Y$
 (-1.5,0) node[draw, line width=1pt](x1) $X_1$
 (1.5,0) node[draw, line width=1pt](x2) $X_2$;
 draw [line width=1pt,-,black] (y) -- (x1);
 draw [line width=1pt,-,black] (y) -- (x2);
 draw [line width=3pt,-,loosely dashed,black] (x1) to[bend right=40] (x2);
 endtikzpicture
endfigure

enddocument

And the resulting figure:

It can clearly be seen that the dash from the X₁ node is longer than that from the X₂ node.

I want the right part of the dashed line to be the mirror image of the left part. Is there a way to do this (preferably regardless of the distance between the nodes, and the thickness or specific pattern of the line)?

There are standard answers, but all of them are very advanced and hard to understand. However, with markings one can "mirror" a half of the curve like this.

documentclass[tikz]standalone
usetikzlibraryshapes,decorations,circuits.logic.US,circuits.logic.IEC,fit,external
tikzstyleloosely dashed=[dash pattern=on 4pt off 8pt]
tikzstyleloosely dashed2=[dash pattern=on 4pt off 8pt]

begindocument
 begintikzpicture[every node/.style = draw=none, text=black, circle, minimum size = 13mm, fill=gray!25]
 path
 (0,3) node(y) $Y$
 (-1.5,0) node[draw, line width=1pt](x1) $X_1$
 (1.5,0) node[draw, line width=1pt](x2) $X_2$;
 draw [line width=1pt,-,black] (y) -- (x1);
 draw [line width=1pt,-,black] (y) -- (x2);
 %draw [line width=3pt,-,loosely dashed,black] (x1.south east) to[bend right=40] (x2.south west);
 path [postaction=
 decorate,
 decoration=
 markings,
 mark=at position 0.5 with coordinate (mid);
 
 ] (x1) to[bend right=40] (x2);
 draw[line width=3pt,-,loosely dashed] ([xshift=-4pt]mid) to[out=180,in=-40] (x1);
 draw[line width=3pt,-,loosely dashed] ([xshift=4pt]mid) to[out=0,in=-140] (x2);
 endtikzpicture
enddocument

Another way is to measure the path and then stretch the dash length a bit in such a way that the path ends with a full on. Please also note that tikzstyle is deprecated.

documentclassarticle
usepackagetikz
usetikzlibrarydecorations.markings
tikzset
 full dash/.style args=on #1 off #2
 decoration=
 markings,
 mark=at position 0 with 
 pgfmathsetmacromystretch((pgfdecoratedpathlength-#1)/(#1+#2))/int((pgfdecoratedpathlength-#1)/(#1+#2))
 pgfmathsetmacromyon#1*mystretch
 xdefmyonmyon
 pgfmathsetmacromyoff#2*mystretch
 xdefmyoffmyoff
 ,
 ,
 preaction=decorate,draw=none,
 postaction=draw,dash pattern=on myon pt off myoff pt
 ,

begindocument

beginfigure
 centering
 begintikzpicture[every node/.style = draw=none, text=black, circle, minimum size = 13mm, fill=gray!25]
 path
 (0,3) node(y) $Y$
 (-1.5,0) node[draw, line width=1pt](x1) $X_1$
 (1.5,0) node[draw, line width=1pt](x2) $X_2$;
 draw [line width=1pt,-,black] (y) -- (x1);
 draw [line width=1pt,-,black] (y) -- (x2);
 draw [line width=3pt,-,full dash=on 3pt off 6pt,black] (x1) to[bend right=40] (x2);
 endtikzpicture
endfigure

enddocument