244-252 S SIFAT-SIFAT GRAPH DENGAN NILAIEIGEN RECIPROCAL

SIFAT-SIFAT GRAPH DENGAN NILAIEIGEN RECIPROCAL

Abstract

In this paper ,only simple graph are considered , A graph G is non singular if its adjacency
matrix A)G) is non singular . A non singular graph G satisfies reciprocal eigenvalue property
( property R) If the riciprocal of each eigenvalue of the adjacency matrix A(G) is also an
eigenvalue of A(G) and G satisfies strong reciprocal eigenvalue property (property SR) If the
riciprocal of each eigenvalue of the adjacency matrix A(G) ) is also an eigenvalue of A(G)
and the both have yhe same multiplicities From the definitions SR implies property R.
Furthermore , for same classes of graph (for example trees ), it is know the these properties
are equivalent , However , the equivalence of these two property is not yet know for any
singular graph , In this paper, it is shown yhay these properties stre not equivalent in
general.