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 $\mathfrak{G}_w$ be a simple undirected weighted graph with adjacency matrix $\mathcal{A}(\mathfrak{G}_w)$. The set of all eigenvalues of $\mathfrak{G}_w$ is called the spectrum of $\mathfrak{G}_w$ denoted by $σ(\mathfrak{G}_w)$. The reciprocal eigenvalue property (or property $\mathcal{R})$ for a nonsingular graph $\mathfrak{G}$ is defined as, if $η \in σ(\mathfrak{G})$ then $\frac{1}{η}\in σ(\mathfrak{G})$. Further, if $η$ and $\frac{1}{η}$ have same multiplicities $\forall ~η\in σ(\mathfrak{G})$ then graph is said to have strong reciprocal eigenvalue property (or property $\mathcal{SR}$. Similarly, a nonsingular graph G is said to have antiÂreciprocal eigenvalue property (or property $-\mathcal{R}$) if $η \in σ(\mathfrak{G})$ then $-\frac{1}{η}\in σ(\mathfrak{G})$ furthermore if $η$ and $-\frac{1}{η}$ have same multiplicities $\forall ~η\in σ(\mathfrak{G})$ then strong antiÂreciprocal eigenvalue property (or property $-\mathcal{SR}$) holds for graph. In this article, classes of weighted noncorona graphs satisfying property $\mathcal{R}$ and property $-\mathcal{SR}$ are studied.