notes summary graphs provide in excellent way to describe the essential features of many applications graphs are mathematical structures and are found to be useful in problem solving they may be implemented in many ways by the use of different kinds of data structures graph traversalsdepth first as well as breadth firstare also required in many applications existence of cycles makes graph traversal challengingand this leads to finding some kind of acyclic subgraph of graph that is we actually reach at the problems of finding shortest path and of finding minimum cost spanning tree problems keywords adjacenttwo vertices in an undirected graph are called adjacent edgesa graph consists of set vwhose members are called the vertices of gtogether with set of pairs of distinct vertices from these pairs are called the edges of free treea free tree is defined as connected undirected graph with no cycles graphgraph is mathematical structure and finds its application in many areas of interest in which problems need to be solved using computers undirected graphif the pairs are unorderedthen is called an undirected graph self assessment fill in the blanks graph may have many the weight of tree is just the sum of weights of its the ends when no more paths are found in an undirected graphpair of vertices representing any edge is in digraph the path is called directed path and cycle as state whether the following statements are true or false dijkstra developed an algorithm to determine the shorted path between two nodes in graph the algorithm is not equally applicable to grapha digraphor even to mixed graph with only some of its sides directed cycle is not path in which first and last vertices are the same good deal of nomenclature is associated with graphs in digraph the path is called directed path and cycle as directed cycle review questions what do you mean by shortest path find out the minimum number of edges in strongly connected diagraph on vertices lovely professional university