Please show full complete proof and answer the question clearly and fully thanks

UNDIRECTED GRAPHS ALGORITHM for good feedback please provide pseudocode with the proof!

(Who's left on the island?) The television production company you work for has created a new spinoff of a popular reality show. Called Survivor: The Traversals, the show works as follows: There are n participants at the beginning of the season. In the first episode, the participants form a certain number of friendships, represented by an undirected graph G on n vertices (one per participant). Friendships do not change after the first episode In every subsequent episode, one participant gets voted off the island. That participant is chosen from among the participants with the least number of friends remaining on the island (In graph terms: in each epsiode choose a vertex from among the vertices with smallest degree in the remaining graph, and delete that vertex. The first season of the show lasts as long as there remains a participant on the island with either zero or one remaining friends (i.e a vertex with degree at most one). As soon as the graph doesn't contain any vertices of degree at most 1, the season ends. Let G denote the graph of friendships among the players remaining at the end of the season. We call G the survivor graph of G For example, if G consisted of just two vertices connected by an edge, then G would be the empty graph (since all the vertices would get deleted). If G consisted of a cycle, then G' would be the same as G. (a) Prove or disprove: (For every undirected graph G,) If G is a tree, then its survivor graph G' is empty (b) Give an algorithm which takes as input a graph G and returns its survivor graph G in time O(m +n), where m is the number of edges in G. (As usual: describe your algorithm in English, give pseudocode, prove it is correct and analyze its running time Hint: There are a few natural approaches. One is to run DFS or BFS and pass over the tree starting with the leaves (be careful: the traversal might start at a vertex that ends up getting deleted). Another approach is to keep a list of all the degree-1 vertices, and update it as vertices are deleted.]