In this paper. we introduce the notion of g-convex weight sequence (gcws) for connected graphs based on the concept of g-convexity and g-weight. g-weight is a natural generalization of the notion of branch weight for trees. We investigate the various questions of realization of an integer sequence as a g-convex weight sequence for trees and some special classes of graphs such as compl... https://www.socialstudiesscholar.com/