What are homeomorphic graphs explain giving an example?

graph theory …graphs are said to be homeomorphic if both can be obtained from the same graph by subdivisions of edges. For example, the graphs in Figure 4A and Figure 4B are homeomorphic.

Which of the following graphs is homeomorphic to?

Two graphs G and G* are said to homeomorphic if they can be obtained from the same graph or isomorphic graphs by this method. The graphs (a) and (b) are not isomorphic, but they are homeomorphic since they can be obtained from the graph (c) by adding appropriate vertices.

Are isomorphic graphs homeomorphic?

If 2 graphs are isomorphic, they are homeomorphic .

How are homeomorphic graphs used in discrete mathematics?

If by graph homeomorphisms we mean the isomorphisms of graph subdivisions (isomorphism after introducing new nodes that subdivide one or more edges), then a necessary (but not always sufficient) criterion asks if the reduced degree sequences of the two graphs (meaning that degree 2 entries are deleted from the degree sequences) are the same.

Which is not an isomorphic graph but a homeomorphic graph?

The graphs (a) and (b) are not isomorphic, but they are homeomorphic since they can be obtained from the graph (c) by adding appropriate vertices. A subgraph of a graph G= (V, E) is a graph G’= (V’,E’) in which V’⊆V and E’⊆E and each edge of G’ have the same end vertices in G’ as in graph G. Note: A single vertex is a subgraph.

Do you need to subdivide graphs to be homeomorphic?

If two graphs are isomorphic, then they are also homeomorphic (no need to “subdivide” edges), but the converse isn’t true. Since subdividing can introduce as many degree 2 vertices as we wish, the criterion of reduced degree sequences equal is necessary but not sufficient for graph homeomorphism.

Which is an example of a homeomorphism problem?

Here it is emphasized that only 2-valent vertices can be smoothed. For example, the simple connected graph with two edges, e1 { u, w } and e2 { w, v }: Determining whether for graphs G and H, H is homeomorphic to a subgraph of G, is an NP-complete problem. The barycentric subdivision subdivides each edge of the graph.