Проверить, является ли заданный граф связным

edge(a, c).
edge(a, b).
edge(c, d).
edge(b, d).
edge(e, d).
 
e(A,B):-edge(A,B);edge(B,A). %budem schitat, chto graf nenapravlenii
 
%vspomogatelnii predikat member(E,L), proveryayushii prinadlezit li element E spisku L
member(H,[H|_]). %esli element raven golove spiska, to rezultat polozitelnii
member(X,[_|Tail]):-member(X,Tail). %esli element vstrechaetsya v hvoste spiska, to rezultat polozitelnii
 
path(A,B,P):-p(A,[B],P).%ishem put ot konechnoi vershini v nachalnuyu. Ishodnii put budet sostoyat iz odnoi konechnoi vershini
 
p(A,[A|Tail],[A|Tail]).%esli tekushaya vershina v nashem puti ravna nachalnoi, to etot put yavlyaetsya iskomim
p(A,[B|Tail],P):-e(B,C,_),not(member(C,Tail)),p(A,[C,B|Tail],P). %B-tekushaya vershina puti
 
%not_connected - vspomogatelnii predicat, proveryayushii est li v grafe nesvyazannaya para vershin
not_connected:- e(A,_),e(B,_), A<>B, not(path(A,B,P)). %istenen, esli est dve vershini, dlya kotorih ne vipolnim predicat path
 
%is_connected
is_connected:-not(not_connected).%graf svyazan, esli net ne svyazannoi pari vershin

edge(a, c).
edge(a, b).
edge(c, d).
edge(b, d).
edge(e, d).
 
e(A,B):-edge(A,B);edge(B,A). %budem schitat, chto graf nenapravlenii
 
%vspomogatelnii predikat member(E,L), proveryayushii prinadlezit li element E spisku L
member(H,[H|_]). %esli element raven golove spiska, to rezultat polozitelnii
member(X,[_|Tail]):-member(X,Tail). %esli element vstrechaetsya v hvoste spiska, to rezultat polozitelnii
 
path(A,B,P):-p(A,[B],P).%ishem put ot konechnoi vershini v nachalnuyu. Ishodnii put budet sostoyat iz odnoi konechnoi vershini
 
p(A,[A|Tail],[A|Tail]).%esli tekushaya vershina v nashem puti ravna nachalnoi, to etot put yavlyaetsya iskomim
p(A,[B|Tail],P):-e(B,C),not(member(C,Tail)),p(A,[C,B|Tail],P). %B-tekushaya vershina puti.
 
%not_connected - vspomogatelnii predicat, proveryayushii est li v grafe nesvyazannaya para vershin
not_connected:-e(A,_),e(B,_),A\=B,not(path(A,B,_)).%istenen, esli est dve vershini, dlya kotorih ne vipolnim predicat path
 
%is_connected
is_connected:-not(not_connected).%graf svyazan, esli net ne svyazannoi pari vershin