| Let G be a simple connected graph with vertex setV {v1, v2,…vn}. Let（d1, d2,…dn）be the degree sequence of G, whered iis the degree ofvi fori=1,2,…n. A non-increasing sequence π=（d1, d2,…dn）is graphic if there exists a graphG of order n such that π is the degree sequence of G, and also called G is a realizationof π. For a given graph H, if there exists a realization of contains H as its subgraph,then π is called potentially H-graphic. Let Ck∪E（Pt）and Ck∪E（C1）be two simplegraphs obtained fromCkby adding the edges of pathPt and cycleCl, respectively. Inthis thesis, the potentiallyC6∪E（P3）-graphic sequences and theC6∪E（C4）-graphicsequences are characterized, respectively. |
