Analyzing the Realization of Degree Sequence by Constructing Orthogonally Diagonalizable Adjacency Matrix.

A finite sequence d: d 1 , d 2 , d 3 ,. .. ., d n of nonnegative integers is said to be graphical if there exists some finite simple graph G, having vertex set V={ v 1 , v 2 , v 3 , …., v n } such that each v i has degree d i (1 ≤ i ≤ n). In this paper we have proposed an algorithm that takes a non-increasing sequence as input and determines whether the given degree sequence is graphic by constructing the adjacency matrix from the given sequence in non-increasing order and checking whether it can be orthogonally diagonalizable. The matrix generated in this process can be used to determine a lot of interesting information regarding the characteristic of the graph directly from the given degree sequence. [ABSTRACT FROM AUTHOR]