Which Traversal Methods Can Be Used To Determine If A Graph Is Connected? We can use a traversal algorithm, either depth-first or breadth-first, to find the connected components of an undirected graph. If we do a traversal starting from a vertex v, then we will visit all the vertices that can be reached from v.
Can Prim’s Algorithm Add Edge Cycle? Note that if A is viable it cannot contain a cycle. Prim’s algorithm operates by repeatedly adding a safe edge to the current spanning tree. Which algorithm specifies the addition of edges to the spanning tree in an increasing order of cost? Kruskal Algorithm addition of edges to Spanning
Does Every Graph With Degree One Have A Cycle? There is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that is joining a node to itself (self-loop) or one of its ancestor in the tree produced by DFS. What is a
Do All Graphs Have Cycles? A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree. How do you know if a graph has a cycle? To detect cycle, check for a cycle in individual trees
Can A Minimum Spanning Tree Contain A Cycle? A spanning tree can never contain a cycle. Spanning tree is always minimally connected i.e. if we remove one edge from the spanning tree, it will become disconnected. A spanning tree is maximally acyclic i.e. if we add one edge to the spanning tree, it will create
Can A Cycle Graph Be A Bipartite? Cycle graphs with an even number of vertices are bipartite. Every planar graph whose faces all have even length is bipartite. Special cases of this are grid graphs and squaregraphs, in which every inner face consists of 4 edges and every inner vertex has four or more neighbors.