Many topological indices for graphs are defined and are widely studied. Some are distance based and some are degree based. They find applications in many fields like chemical graph theory and networking. The concept of transit of a vertex and transit index of a graph was defined by the authors in their previous work. The transit of a vertex v is "the sum of the lengths of all shortest path with v as an internal vertex" and the transit index of G is T I(G) is the sum of the transit of all

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... s of G. In this paper we introduce the concept of majorized shortest path, transit decomposition of a graph and transit decomposition number.