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Eigenvalues of the k ‐th power of a graph
Author(s) -
Das Kinkar Ch.,
Guo JiMing
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500183
Subject(s) - mathematics , combinatorics , spectral radius , graph , discrete mathematics , graph energy , distance regular graph , graph power , upper and lower bounds , eigenvalues and eigenvectors , line graph , mathematical analysis , physics , quantum mechanics
The k ‐th power of a graph G , denoted by G k , is a graph with the same set of vertices as G such that two vertices are adjacent in G k if and only if their distance in G is at most k . In this paper, we give the bounds on the spectral radius of T k andG k( k ≥ 1 ) . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph G k is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.