If we consider the G as the whole of the cycle graph having 4 edges then is G a complete graph?
A cycle graph is like a polygons with vertices along the circumference.
A complete graph is one where EACH vertex is connect to EVERY OTHER vertex (except itself).
Using these definitions, are you able to answer the question?
MathMate: No I am not able to answer this question because I am quite confused between what shapes you can use to draw them up as a cycle graph and complete graph. Also, its a little confusing to me as to how many edges each vertex should have when it comes to cycle graph or complete graph.
To determine if the cycle graph G with 4 edges is a complete graph, we need to understand the definition of a complete graph.
A complete graph is a simple undirected graph where each pair of distinct vertices is connected by a unique edge.
In the case of G, which is a cycle graph with 4 edges, it consists of a single cycle where each vertex is connected to its immediate neighbors by an edge.
Since G only has one cycle and not all pairs of distinct vertices are connected by unique edges, G is not a complete graph.
To confirm this, we can use the formal definition of a complete graph and check if every pair of distinct vertices in G is connected by a unique edge. In G, we can observe that vertices 1 and 3 are not connected by a unique edge because they share the same edge with vertex 2.
Hence, based on the definition and observation, we can conclude that G is not a complete graph.