What is the graph K4?

What is the graph K4?

K4 is a maximal planar graph which can be seen easily. In fact, a planar graph G is a maximal planar graph if and only if each face is of length three in any planar embedding of G. Corollary 1.8. 2: The number of edges in a maximal planar graph is 3n-6.

What is the complement of the given graph?

Complement of Graph in Graph Theory- Complement of a graph G is a graph G’ with all the vertices of G in which there is an edge between two vertices v and w if and only if there exist no edge between v and w in the original graph G.

How many edges are there in the complementary graph of the cube graph q4?

The graph Q3 is the 1-skeleton of a cube, a cubical graph, a planar graph with eight vertices and twelve edges.

What is the chromatic number for K4?

Kawarabayashi, B. Toft, Any 7-chromatic graph has K7 or K4,4 as a minor, Combinatorica 25 (2005) 327–353] and Kawarabayashi, Luo, Niu and Zhang [K.

How many edges are there in K4?

In the case of K4, Bollobás’ example is the following: let F be an n-vertex K4-free graph with two vertices adjacent to all other vertices which form an independent set. This graph has only 2n − 3 edges, and yet all edges in F are K4-saturating edges.

What is p4 in graph theory?

Abstract. A graph is said to be P4-connected if for every partition of its vertices into two nonempty disjoint sets, some P4 in the graph contains vertices from both sets in the partition. A P4-chain is a sequence of vertices such that every four consecutive ones induce a P4.

How do you find the complement of a simple graph?

Complement of Graph

  1. Let ‘G−’ be a simple graph with some vertices as that of ‘G’ and an edge {U, V} is present in ‘G−’, if the edge is not present in G.
  2. |E(G)| + |E(‘G-‘)| = |E(Kn)|, where n = number of vertices in the graph.

What is the diameter of a graph?

The diameter of graph is the maximum distance between the pair of vertices. It can also be defined as the maximal distance between the pair of vertices. Way to solve it is to find all the paths and then find the maximum of all. 4.

How do you find the edges of a complement graph?

What is meant by complement of a graph find the complement of the C5 graph?

In graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G. The complement is not the set complement of the graph; only the edges are complemented.