Non-isomorphic graphs with common degree sequences
Abstract:For all positive even integers n, graphs of order n with degree sequence Sn:1,2,…,n/2,n/2,n/2+1,n/2+2,…,n−1 naturally arose in the study of a labeling problem in [1].This fact motivated the authors of the aforementioned paper to study these sequences and as a result of this study they proved that there is a unique graph of order n realizing Sn for every even integer n. The main goal of this paper is to generalize this result.