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MARIO EZEQUIEL GARCIA HUERTA
Actividad 1 / Unidad 2 / Conceptos fundamentales
ES1421008916
CONTESTA LAS SIGUIENTES PREGUNTAS
Menciona tres situaciones en las que un grafo pueda ser útil.
1. Para el diseño de bases de datos.2. Para el diseño de redes.3. Para orientar las vías públicas.
¿Será posible hacer grafos del funcionamiento del cuerpo humano?
Si de hecho los neurólogos lo utilizan para el estudio de las neuronas.
Grafo
Se representa como:Matriz incidencia
MAtriz adyacencia
Puede ser:ciclo
caminocadena
Grafos Dirigidos se representa:
Puntos y flechas
Grafos no dirigidos se representa
Puntos y lineas
Integra los conceptos estudiados, analiza la gráfica (grafo) resultante y menciona sus características.
• Es un grafo no dirigido• Pares no ordenados• Grafo simple
¿Cuántas aristas tiene el grafo?31 Aristas
¿Cuántos vértices tiene el grafo?18 Vértices
Determina la matriz de incidencia y adyacencia.Matriz de incidencia
e01 e02 e03 e04 e05 e06 e07 e08 e09 e10 e11 e12 e13 e14 e15 e16 e17 e18 e19 e20 e21 e22 e23 e24 e25 e26 e27 e28 e29 e30 e31
V01[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V02[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V03[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V04[0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V05[0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V06[0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V07[0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V08[0,0,0,0,0,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
V09[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0]
V10[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,1,1,0]
V11[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1]
V12[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1]
V13[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
V14[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0]
V15[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
V16[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
V17[0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
Matriz de adyacencia
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,1]
[0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0]
[0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,0,1,0]
[0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0]
[0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,0]
[0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1]
[0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,1,0,1]
Realiza el grafo de Sinaloa, siguiendo los comandos asignados por el programa que elijas:
CALCULOS REALIZADOS CON EL PROGRAMA MAXIMA
/*Creamos el Grafo del Estado de Sinaloa*/sinaloa: create_graph([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],
[ [1,2],[2,3],[2,4],[3,4],[4,5],[5,6],[5,7],[6,7],[6,8],[7,8],[8,9],[8,17],[8,18],[9,10],[9,17],[10,11],[10,12],[10,13],[10,14],[10,15],[10,17],[11,12],[12,13],[13,14],[14,15],[14,16],[15,16],[15, 17], [16, 17], [16, 18], [17, 18]]);
GRAPH\ (18 vertices, 31 edges\)
/*Desplegamos una vista alterna para ver la interacción de los vértices y así darnos una idea de la estructura del grafo, esta representación nos muestra los nodos hijos a la derecha de los padres.*/
print_graph(sinaloa)$
Graph on 18 vertices with 31 edges. Adjacencies:
1 : 22 : 4 3 13 : 4 24 : 5 3 25 : 7 6 46 : 8 7 57 : 8 6 58: 18 17 9 7 69: 17 10 8
10: 17 15 14 13 12 11 911: 12 1012: 13 11 1013: 14 12 1014: 16 15 13 1015: 17 16 14 1016: 18 17 15 1417: 18 16 15 10 9 818: 17 16 8
/*Otra manera alternativa de mostrar la estructura de un grafo es mediante la siguiente función*/
draw_graph(sinaloa, show_id=true,vertex_color="yellow")$
/*Para determinar el camino más corto entre los vértices 1 y 11 tenemos:*/
sh: shortest_path(1,11,sinaloa); [1,2,4,5,7,8,17,10,11]
/*Graficando el recorrido del vertice 1 al 11*/ draw_graph(sinaloa,show_edges = vertices_to_path(sh), show_id = true,head_length = 0.05,vertex_color="yellow")$
/*Calculo de la matriz de adyacencia*/ adjacency_matrix(sinaloa);
matrix [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0])
Referencias:
Primeros pasos en máxima http://maxima.sourceforge.net/docs/tutorial/es/max.pdf
Manual Máxima http://maxima.sourceforge.net/docs/manual/es/maxima.pdf
Mapa Sinaloa http://cuentame.inegi.org.mx/juegos/sin/sin.html