have a number 5 b or each vertex hs 12
❖ Definition 8: Graphs that have a number assigned to each edge or each vertex are called weighted graphs ❖ weighted digraphs
o Definition 9: The graph G(V,E) is s caned a subgraph of G(vE) If Vcv and EcE. If V=V, then G(,E) is said to be a spanning subgraph. v2 4 (a)G (b)subgraph G (spanning subgraph G
❖ Definition 9: The graph G'(V',E') is called a subgraph of G(V,E) If V'V and E'E. If V'=V, then G'(V,E') is said to be a spanning subgraph
Definition 10: If G(V,E) contains all edges of G that ioin two vertices in V then g is called the induced subgraph by v'cv and is denoted b G(V") go induced subgraph by ( v1v2 v4, v5 induced subgraph by IVi,V2, Va,v5
❖ Definition 10: If G'(V',E') contains all edges of G that join two vertices in V' then G' is called the induced subgraph by V'V and is denoted by G(V'). ❖ induced subgraph by {v1 ,v2 ,v4 ,v5 }
Definition 11: The complement of a graph g is the graph(denoted G) with the same vertex set but whose edge set consists of the edges not present in G(i.e, the complement of the edge set of G with respect to all possible edges on the vertex set of g) K
Definition 11: The complement of a graph G is the graph (denoted G ) with the same vertex set but whose edge set consists of the edges not present in G (i.e., the complement of the edge set of G with respect to all possible edges on the vertex set of G)
8G-v, or G-iv .o When we remove a vertex v from a graph, we must remove all edges incident with the vertex v When a edge is removed from a graph, without removing endpoints of the edge G
❖ G-v, or G-{v} ❖ When we remove a vertex v from a graph, we must remove all edges incident with the vertex v. ❖ When a edge is removed from a graph, without removing endpoints of the edge