I read the code in the link below and have some thoughts on drawing the graph.

https://www.mapleprimes.com/questions/216092-Options-For-Graph-Drawing-In-The-GraphTheory

with(GraphTheory):

with(SpecialGraphs):

G := PetersenGraph();:

POS := GetVertexPositions(G);

EG := Edges(G);

PLOT(

seq( CURVES([POS[EG[i][1]], POS[EG[i][2]]], LINESTYLE(3) ), i=1..numelems(Edges(G))),

POINTS(POS, SYMBOL(_SOLIDBOX, 35), COLOR(RGB, 1, 1, 0)),

seq(TEXT(POS[i], i), i=1..numelems(Vertices(G))),

AXESSTYLE(NONE)

)

But if we want to change the edge to a curvilinear style, it seems very difficult. We know **PetersenGraph** is **1-planar graph**. The following picture is one of its 1-plane drawing. That is also what I want to draw .

**PS: **A **1-planar graph** is a graph that can be drawn in the Euclidean plane in such a way that each edge has **at most one crossing point**, where it crosses **a single additional edge**.

Although I asked a similar question, but it uses too many special **curve functions and the method is relatively isolated.** Because the cycle graph is too special. https://www.mapleprimes.com/questions/228987--Can-We-Draw-Curved-Edges-In-The-Graph

I also noticed the optional items of the edge style. But there are no curves, such as **arcs, parabola, **etc.

**The plot style must be one of line, point, pointline, polygon (patchnogrid), or polygonoutline (patch). **

I am trying to draw a parabola, it seems to be quite difficult. And it completely deviated from the use of graph theory package.

drawarc :=proc(A,B,C,ecolor);

local c,ax,cx ,ay,cy,ox,oy,oo,x,y,b,a,an_end,an_start,r,yuanhu:

ax :=evalf(geometry)[HorizontalCoord](A):

cx :=evalf(geometry)[HorizontalCoord](C):

ay :=evalf(geometry)[VerticalCoord](A):

cy :=evalf(geometry)[VerticalCoord](C):

geometry[circle](c,[ A ,B ,C], [x,y],'centername' =o):

ox :=evalf(geometry[HorizontalCoord] (o)):

oy :=evalf(geometry[ VerticalCoord] (o)):

if(cx -ox)>0 then

b :=arctan((cy -oy) /(cx -ox)):

elif(cx -ox)=0 and (cy -oy)>0 then

b :=Pi/2 :

elif(cx -ox)=0 and (cy -oy)<0 then

b :=-Pi/ 2 :

else

b :=Pi +arctan((cy -oy) /(cx -ox)):

fi :

if(ax -ox)>0 then

a :=arctan((ay -oy) /(ax -ox)):

elif(ax -ox)=0 and (ay -oy)>0 then

a :=Pi /2 :

elif(ax -ox)=0 and (ay -oy)<0 then

a :=-Pi/ 2 ;

else

a :=Pi +arctan((ay -oy)/ (ax -ox)):

fi ;

if(evalf(b)<evalf(a))then

an_start :=a :

else

an_start :=a +2*Pi :

fi :

an_end :=b :

r :=geometry[ radius] (c);

yuanhu :=plottools[ arc] ([ ox , oy] , r , an_start..an_end):

plots[ display] (yuanhu , scaling =constrained, color =ecolor,axes=none);

end :

geometry[point] (a , -3 .00 , 1 .70);

geometry[point] (b , 0 .35 , -0 .45);

geometry[point] (c , 3 .13 , 1 .86);

l :=[a , b , c] ;

drawarc(a,b,c,blue);

I would like to ask maple if there is a more versatile and simpler way to draw a curve of graph drawing.

local i , num , arcs , arc_text , vl , display_set ;

vl :=VL ;

num:=nops(vl);

arcs :={};

i:=1;

if num <3 then

"There isn' t enough points in the point list." ;

return ;

elif irem(num-1 , 2)<>0 then

"The number of the list must be multiple of 2 when it minus 1 .";

fi :

while i <num do

arcs :={drawarc(vl[i] ,vl[i +1] , vl[i +2],ecolor),op(arcs)};

i:=i +2 ;

od ;

arc_text :=geometry[ draw] ({vl[1] , vl[num] }, printtext =true , color =ecolor);

display_set:={op(arcs),arc_text};

plots[ display] (display_set , view =[ -abs(scope)..abs(scope), -abs(scope)..abs(scope)] , scaling =constrained,axes=none);

end proc:

geometry[ point] (v1 , 0 ,0):

geometry[ point] (a , 3, 9):

geometry[ point] (b , 7, 9):

geometry[ point] (c, 6,8):

geometry[ point] (d , 12,9):

geometry[ point] (e , 7 ,2):

geometry[ point] (v3 , 9 ,0):

vl:=[ v1,a,b,c,d,e,v3] :

drawarcs(vl,red,20);

The above program is too cumbersome and not robust

with(GraphTheory):

with(SpecialGraphs):

G := PetersenGraph():

POS := GetVertexPositions(G):

EG := Edges(G) minus {{6,10},{6,7}}:

s1:=PLOT(

seq( CURVES([POS[EG[i][1]], POS[EG[i][2]]], LINESTYLE(3) ), i=1..numelems(Edges(G))-2),

POINTS(POS, SYMBOL(_SOLIDBOX, 35), COLOR(RGB, 1, 1, 0)),

seq(TEXT(POS[i], i), i=1..numelems(Vertices(G))),

AXESSTYLE(NONE)

):

geometry[ point] (a,op(GS(G)[6])):

geometry[ point] (b , op(GS(G)[7])):

geometry[ point] (c , op(GS(G)[10])):

geometry[ point] (d ,op(GS(G)[8])[1]+0.3,op(GS(G)[8])[2]-0.5):

geometry[ point] (d2 ,op(GS(G)[9])[1]-0.3,op(GS(G)[9])[2]-0.5):

s2:=drawarc(a,d,b,red):

s3:=drawarc(c,d2,a,red):

plots:-display({s1,s2,s3});