On weighted noncorona graphs with properties R and −SR: 10.48129/kjs.17497 - Ahmad, Uzma; Hameed, saira; Akhtar, sadia (Kuwait Journal of Science, 2023)
Let G_w be a simple undirected weighted graph with adjacency matrix A(G_w). The set of all eigenvalues of G_w is called the spectrum of G_w denoted by σ(G_w). The reciprocal eigenvalue property (or property R) for a nonsingular graph G is defined as, if η σ(G) then 1ησ(G). Further, if η and 1η have same multiplicities ησ(G) then graph is said to have strong reciprocal eigenvalue property (or property SR. Similarly, a nonsingular graph G is said to have antiÂreciprocal eigenvalue property (or property -R) if η σ(G) then -1ησ(G) furthermore if η and -1η have same multiplicities ησ(G) then strong antiÂreciprocal eigenvalue property (or property -SR) holds for graph. In this article, classes of weighted noncorona graphs satisfying property R and property -SR are studied.