Grafo bandera

Grafo bandera
Vértices 5
Aristas 5
Radio 2
Diámetro 3
Cintura 4
Automorfismos 2 (Z/2Z)
Número cromático 2
Índice cromático 3
Propiedades
[editar datos en Wikidata]

En el campo matemático de la teoría de grafos, el grafo bandera [1]​ es un grafo plano simple con 5 vértices y 5 aristas. Su nombre es debido a su semejanza a una bandera. Es parte del catálogo de grafos pequeños del Information System on Graph Classes and their Inclusions.[2]​

Propiedades generales

Es plano, ya que puede representarse en el plano sin que sus aristas se crucen. Es 1-conexo por vértices y tiene un vértice de corte. Es un pseudoárbol también llamado 1-árbol

Coloración

El número cromático del grafo bandera es 2. Esto es, que es posible colorear los vértices con dos colores tal que dos vértices conectados por una arista tengan siempre colores diferentes.

El índice cromático del grafo es 3. Esto es, existe una 3-coloración por aristas del grafo tal que dos aristas incidentes a un mismo vértice son siempre de colores diferentes.

El polinomio cromático es igual a .

Propiedades algebraicas

El grupo de automorfismo del grafo bandera es isomorfo al grupo abeliano de orden 2, Z/2Z.

El polinomio característico del grafo es : .

Véase también

Referencias

  1. ↑ Weisstein, Eric W. «Banner Graph». En Weisstein, Eric W, ed. MathWorld (en inglés). Wolfram Research. 
  2. ↑ ISGCI (Information System on Graph Classes and their Inclusions), Lista de grafos pequeños (caché) (en inglés).

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