Bevezet\303\251s a matematik\303\241ba
J\303\241rai Antal
Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak.
2. Term\303\251szetes sz\303\241mok
7. Gr\303\241felm\303\251let
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
7.1. Ir\303\241ny\303\255tatlan gr\303\241fok
7.1.1. Ir\303\241ny\303\255tatlan gr\303\241fok.
restart;
with(networks);
new(G1):addvertex({v1,v2,v3,v4,v5},G1);
addedge([{v1,v2},{v1,v2},{v1,v4},{v3,v4},{v4,v4}],G1);
edges(G1);vertices(G1);
ends(e2,G1);
edges({v1,v2},G1);
incident(v1,G1);incident(v5,G1);
neighbors(v1,G1);neighbors(v4,G1);
vdegree(v1,G1);vdegree(v4,G1);vdegree(v5,G1);degreeseq(G1);mindegree(G1);maxdegree(G1);
show(G1);
G:=void(10):vertices(G);edges(G);
addedge([{1,2},{2,3},{3,4}],names=[cica,alma,kutya],G);show(G);
G:=petersen():draw(G);degreeseq(G);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
7.1.13. P\303\241ros gr\303\241fok.
new(G22):addvertices([H1,H2,H3,K1,K2,K3],G22);connect({H1,H2,H3},{K1,K2,K3},G22);draw(G22);
G:=complete(3,3):draw(G);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
7.1.15. R\303\251szgr\303\241f.
show(G);
delete({e4},delete({1},G)):vertices(%);edges(%%);draw(%%%);
show(G1);
new(G3):addvertex({v1,v2,v3,v4},G3);addedge([{v1,v2},{v2,v3},{v1,v4},{v2,v4}],G3);draw(G3);
draw(complement(G3));
induce({v2,v3,v4},G3):draw(%);
induce({e2,e1,e4},G3):draw(%);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
7.1.19. S\303\251t\303\241k, vonalak, utak, k\303\266r\303\266k.
G4:=void(9):addedge(Path(1,2,3,4,5,6,7,3,8,9,8),G4);show(G4);
G:=void(5):addedge(Cycle(1,2,3,4,5),G);draw(G);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
*7.1.58. Feladat: Dirac t\303\251tele.
7.1.60. C\303\255mk\303\251zett \303\251s s\303\272lyozott gr\303\241fok.
new(G9):addvertex([v1,v2,v3,v4],weights=[2,4,6,8],G9);addedge([{v1,v2},{v2,v3},{v1,v3},{v3,v4}],weights=[1,1,1,3],G9);show(G9);
*7.1.65. Feladat: a k\303\255nai post\303\241s-probl\303\251ma.
*7.1.66. Feladat: az utaz\303\263 \303\274gyn\303\266k probl\303\251m\303\241ja.
7.1.67. Tov\303\241bbi feladatok.
7.2. Ir\303\241ny\303\255tott gr\303\241fok
7.2.1. Ir\303\241ny\303\255tott gr\303\241fok.
restart;with(networks);
G:=void(6):addedge([[1,2],[2,4],[1,3],[3,6],[2,6],[1,5]],G);
tail(e1,G);head(e1,G);
indegree(2,G);outdegree(2,G);
addedge([1,2],G);tail(%,G);head(%%,G);
show(G);
7.2.16. Ir\303\241ny\303\255tott fa.
7.2.17. K\303\266nig-lemma.
*7.2.24. Dinamikus programoz\303\241s.
*7.2.36. Folyamprobl\303\251ma.
*7.2.38. Ford-Fulkerson-t\303\251tel (maxim\303\241lis folyam, minim\303\241lis v\303\241g\303\241s t\303\251tel).
*7.2.39. Edmonds-Karp-heurisztika.
*7.2.43. Feladat: \303\241ltal\303\241nos\303\255tott folyamprobl\303\251ma.
*7.2.44. Feladat: Menger t\303\251tele elv\303\241g\303\263 \303\251lhalmazra.
*7.2.45. Feladat: Menger t\303\251tele elv\303\241g\303\263 cs\303\272cshalmazra.
*7.2.46. Feladat: K\303\266nig t\303\251tele.
*7.2.56. Gr\303\241fok topologikus izomorfizmusa.
7.2.63. Kromatikus sz\303\241m.
7.2.71. Tov\303\241bbi feladatok.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn