Abstract Let Γ denote a finite, bipartite, connected graph with vertex set X. Fix x X x ∈ X and let 3 ε ≥ 3 denote the eccentricity of x. For mutually distinct scalars \ ^*ᵢ\₈=₀^ θ i ∗ i = 0 ε define a diagonal matrix A^*=A^* (^*₀, ^*₁, , ^*) {\, Mat\, }X (R) A ∗ = A ∗ (θ 0 ∗, θ 1 ∗, …, θ ε ∗) ∈ Mat X (R) as follows: for y X y ∈ X set (A^*) ₘₘ = ^* (ₗ, ₘ) (A ∗) yy = θ ∂ (x, y) ∗, where ∂ denotes the shortest path-length distance function of Γ. We say that A^* A ∗ is a dual adjacency matrix candidate of Γ
Fernández et al. (Mon,) studied this question.
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