7. I think it also may depend on whether we have and even or an odd number of vertices? possible edges. Given an array edges where edges[i] = [type i, u i, v i] represents a bidirectional edge of type type i between nodes u i and v i, find the maximum number of edges you can remove so that after removing the edges, the graph can still be fully traversed by both Alice and Bob. Make an adjacency matrix A. where A[i][j] is 1 if there is an edge between i and j, and 0 otherwise.. Then, the number of paths of length k between i and j is just the [i][j] entry of A^k.. The main result is Theorem 1. Section 4.3 Planar Graphs Investigate! If n is the number of vertices of G, then the number of edges in a k-regular graph is nk/2. Problem-04: A graph has 24 edges and degree of each vertex is k, then which of the following is possible number of vertices? 1.10 Give the set of edges and a drawing of the graphs K 3 [P 3 and K 3 P 3, assuming that the sets of vertices of K 3 and P 3 are disjoint. EXERCISE: Draw two 3-regular graphs with six vertices. ksuch that v iv i+1 is an edge for each i= 1;:::;k 1. Regular Graph. In another direction, Broere et al. number of edges whose removal from G results in a disconnected graph or in the trivial graph (=a single vertex). It follows from the above that the graph is regular of order n. However, if we just multiplied the number of vertices by the degree, we would count every edge twice, so we must take one half of this: Number of edges = 2^n * n / 2 = n * 2^(n-1) In general, a complete bipartite graph is not a complete graph. Discrete Mathematics 48 (1984) 197-204 197 North-Holland REGULAR GRAPHS AND EDGE CHROMATIC NUMBER R.J. FAUDREE Memphis State University, Memphis, TN38152, USA J. SHEEHAN University of Aberdeen, The Edward Wright Building, Aberdeen, UK Received 23 September 1982 Revised 12 April 1983 For any simple graph G, Vizing's Theorem [5] implies that A (G)~)((G)<~ A(G)+ 1, where A … The matching number, denoted µ(G), is the ... a matching saturatingA. In graph theory, graphs can be categorized generally as a directed or an undirected graph.In this section, we’ll focus our discussion on a directed graph. Which of the following statements is false? 78 CHAPTER 6. 05, Apr 19. a. The vertices and edges in should be connected, and all the edges are directed from one specific vertex to another. So the number of edges is just the number of pairs of vertices. gave a formula for the minimum size of a matching among k-regular (k − 2)-edge-connected graphs with a fixed number of vertices (see also ). Clearly, we have ( G) d ) with equality if and only if is k-regular for some . bidden subgraphs for 3-regular 4-ordered hamiltonian graphs on more than 10 vertices. Solution: The regular graphs of degree 2 and 3 are shown in fig: Example1: Draw regular graphs of degree 2 and 3. Lemma 1 (Handshake Lemma, 1.2.1). On the other hand if no vivj, 2 6i