The generalized path matrix and energy
Pengli Lu, Rui Luan
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Source: Crossref
Published: Mar 10, 2022
DOI: 10.1142/s1793830922500719
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We define the path Laplacian matrix and the path signless Laplacian matrix of a simple connected graph G as [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the path matrix and [Formula: see text] is the diagonal matrix of the vertex transmissions. The generalized path matrix is [Formula: see text], for [Formula: see text] and [Formula: see text] are the eigenvalues of [Formula: see text]. The generalized path energy can be expressed as [Formula: see text], where [Formula: see text] is the path Wiener index of G. We give basic properties of generalized path matrix [Formula: see text]. Also, some upper and lower bounds of the generalized path energy of some graphs are studied.
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