Weighted undirected graph

Question

Consider a Weighted undirected graph connected with 'V'  vertices and 'E' edges.What is the worst case time complexity to check if 2 particular vertices 'x' and 'y' are present in the graph, if present then calculate the minimum distance between them?

Comments

dijkstra's can be modified to output shortest path with minimum edges. 

https://stackoverflow.com/questions/20041931/find-the-shortest-path-with-the-least-number-of-edges

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@junk_mayavi

https://www.fi.muni.cz/~hlineny/Vyuka/GT/Grafy-lect-en-3.pdf

Distance in weighted graph is considering the weights of the edges.

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@VS thank you... I was wrong about weighted distance concept :)