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