Geodesic
Sequences of Maximal Degree Vertices in Graphs
Serdica Mathematical Journal, Tome 30 (2004) no. 1, pp. 95-102.

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Let Γ(M ) where M ⊂ V (G) be the set of all vertices of the graph G adjacent to any vertex of M. If v1, . . . , vr is a vertex sequence in G such that Γ(v1, . . . , vr ) = ∅ and vi is a maximal degree vertex in Γ(v1, . . . , vi−1), we prove that e(G) ≤ e(K(p1, . . . , pr)) where K(p1, . . . , pr ) is the complete r-partite graph with pi = |Γ(v1, . . . , vi−1) Γ(vi )|.
Keywords: Maximal Degree Vertex, Complete S-partite Graph, Turan’s Graph 
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Khadzhiivanov, Nickolay; Nenov, Nedyalko. Sequences of Maximal Degree Vertices in Graphs. Serdica Mathematical Journal, Tome 30 (2004) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_1_a7/