Universal Distance Spectra of Join of Graphs
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i1.5019Keywords:
Universal distance spectrum, Seidal matrix, Joined Union, Complete split graphAbstract
Consider G a simple connected graph. In this paper, we introduce the Universal distance matrix UD (G). For α, β, γ, δ ∈ R and β ̸= 0, the universal distance matrix UD (G) is defined as
UD (G) = αTr (G) + βD(G) + γJ + δI,
where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitrary graph H. As a consequence, we obtain the eigenvalues of distance matrix, distance Laplacian matrix, distance signless Laplacian matrix, generalized distance matrix, distance Seidal matrix and distance matrices of complementary graphs.
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