Consider an undirected graph G=(V,E) where every edge e has a given cost C e . A

Question

Consider an undirected graph G=(V,E) where every edge e has a given cost Ce. Assume that all edge costs are positive and distinct. Let T be a minimum spanning tree of G and P be a shortest path from the vertex s to the vertex t. Now suppose that the cost of every edge of G is increased by 1 (for each edge: Ce=Ce+1). Call this new graph G.

Is T a minimum spanning tree of G?
Is P the shortest s-t path of G?

Consider an undirected graph G (V, E) where every edge e has a given cost ce Assume that all edge costs are positive and distinct. Let T be a minimum spanning tree of G and P be a shortest path from the vertex s to the vertext. Now suppose that the cost of every edge of G is increased by 1 (for each edge: ce ce 1). Call this new graph G Is T a minimum spanning tree of G'? Is Pthe shortest s-t path of G

Explanation / Answer

consequently a graph G(V, E) is known which have separate edges then this income that the haggard on both sides of tree resolve be a unique one. So condition we enlarge the cost of each edge in G then the achieve graph G' resolve be a unique graph, This income that the on both sides of tree achieve from G' will be unique. So we be able to end that T still a MST of G'. P will stay as straight s to t path in G' as well. But the cost between s to t will increase depending on how a lot of vertices are in between or how a lot of edges are between them.

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