On The Turan Number Of PG And Some Explorations Of The Characterization Of The Degree Sequences Of3-trees

The Turan number ex(m, G) of the graph G is the maximum number of edges of an m-vertex simple graph having no G as a subgraph. A star Sr is the complete bipartite graph K1,r (or a tree with one internal vertex and r leaves). Let Pn be the path on n vertices and pG denote the disjoint union of p copies of G. If G=S2, Gorgol conjectured that ex(m,pS2)=[m-P+1/2]+(p-1)m-(p2) for m sufficently large.The degree sequence of a graph is the sequence of the degrees of its vertices. If D is the degree sequence of a graph G, then G is a realization of D and G realizes D. A graph G is a k-tree if either G is the complete graph on k+1vertices, or G has a vertex v whose neighborhood is a clique of order k and the graph obtained by removing v from G is a k-tree.In this thesis, we obtain the following results:1. Determine the Turan number of pSr, and show that Gorgol’s conjecture is true.2. Determine the Turan number of P4and the Turan number of pP4.3. Explore the characterization of the degree sequences of3-trees.