Construction and Nullity of Some Classes of Smith Graphs

2018-10

2018 International Conference on Advanced Science and Engineering (ICOASE)

or the adjacency matrix A of a graph G, a number
is an eigenvalue of G if for some non zerovector X, AX=X. The
vector X is called the eigenvector corresponding to . The
eigenvalues are exactly those numbers that make the matrix A-
I to be singular. All eigenvectors corresponding to forms a
subspace V; the dimension of V is equal to the multiplicity of .
A graph G is a Smith graph if 2 is an eigenvalue of the adjacency
matrix A of G, a -weighting technique is introduced and applied
to characterize some classes of Smith graphs as well as to study
their nullities and the nullity of vertex identification of such
graphs. We also have proved that under certain conditions t