I would like to know if there is an upper bound on the length of the shortest paths between vertices on an undirected and unweighted graph based on degree of vertices, number of vertices and number of edges. I consider the shortest paths. So path length is smaller than the number of vertices. I want to know if I can get a better bound with the information of degrees of vertices.
Specifically I have a graph where degree of each vertex is either 1, 2 or 3.