| A variation of classical Turan-type extremal problems is considered as follows:for a given graph H, determine the smallest even integerσ(H, n) such that every n-term graphic sequenceπ=(d1,d2,…,dn) with term sumσ(π)= d1+d2+…+dn≥σ(H,n) has a realization G containing H as a subgraph. Let Fm1,…,mk;r denote the more generalized friendship graph on m1+…+mk+r vertices, that is, the graph of Kr+m1,…,Kr+mk meeting in a common r set, where Kr+mi is the complete graph on r+mi vertices. This thesis mainly considers the problem of determining the values ofσ(Fm1,…,mk;r, n), and obtain the following results:1. Determining the values ofσ(F2k1,1k2;1,n) for k1≥1, k2≥1 and n sufficiently large;2. Characterizing the potentially F23;1 graphic sequences;3. Determining the values ofσ(Fm1,…,mk;r, n) for n sufficiently large. |
