Affiliation: | a Department of Mathematics and Statistics, Georgia State University, United States b Department of Theoretical and Applied Mathematics, The University of Akron, United States c Department of Mathematics and Computer Science, Emory University, United States d Department of Mathematics, Middlebury College, United States |
Abstract: | A nonincreasing sequence of nonnegative integers π=(d1,d2,…,dn) is graphic if there is a (simple) graph G of order n having degree sequence π. In this case, G is said to realizeπ. For a given graph H, a graphic sequence π is potentiallyH-graphic if there is some realization of π containing H as a (weak) subgraph. Let σ(π) denote the sum of the terms of π. For a graph H and n∈Z+, σ(H,n) is defined as the smallest even integer m so that every n-term graphic sequence π with σ(π)≥m is potentially H-graphic. Let denote the complete t partite graph such that each partite set has exactly s vertices. We show that and obtain the exact value of σ(Kj+Ks,s,n) for n sufficiently large. Consequently, we obtain the exact value of for n sufficiently large. |