Abstract
A sequence π = (d1, d2,..., dn) of non-negative integers is said to be graphic if it is the degree sequence of a simple G on vertices, and such a graph G is referred to as a realization of π. The set of all non-increasing non-negative integer sequences π = (d1, d2,..., dn) is denoted by NSn. A sequence π∊NSn is said to be graphic if it is the degree sequence of a graph G on vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NSn is denoted by GSn. A split graph Kr + Ks on r + s vertices is denoted by Sr,s. A graphic sequence π is potentially H-graphic if there is a realizaton of π containing H as a subgraph. In this paper, we determine the graphic sequences of subgraphs H, where H is Sr1 ,s1 + Sr2,s2 + Sr3,s3 + ... + Srm, sm, Sr1,s1 V Sr2,s2 V ... V Srm,sm and Sr1,s1 X Sr2,s2 X ... X Srm, sm and +, V and x denotes the standard join operation, the normal join operation and the cartesian product in these graphs respectively.
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