Let G = (V, E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint sub graphs G1, G2, ..., Gn of G such that every edge of G belongs to exactly one Gi , (1 ≤ i ≤ n) . The decomposition π = {G1, G2, ....Gn } of a connected graph G is said to be an edge geodetic self decomposi- tion if ge (Gi ) = ge (G), (1 ≤ i ≤ n).The maximum cardinality of π is called the edge geodetic self decomposition number of G and is denoted by πsge (G), where ge (G) is the edge geodetic number of G. Some general properties satisfied by this concept are studied. Connected graphs which are edge geodetic self decomposable are characterized.
Forcing Total Outer Independent Edge Geodetic Number of a Graph
