Amplified eccentric connectivity energy of a graph
Abstract
In this paper, we introduce and formalize the concept of amplified eccentric–connectivity energy
(AECE), a novel spectral graph invariant that combines both local and global structural properties through
a degree–eccentricity weighted adjacency matrix, termed the amplified eccentric–connectivity matrix. We
investigate the spectral properties of this matrix and exact analytical expressions for AECE are derived for
key graph classes.
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