Energy of a graph is never the square root of an odd integer | Zendy

S. Pirzada | Zendy; Iván Gutman | Zendy

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Energy of a graph is never the square root of an odd integer

Author(s) -

S. Pirzada,

Iván Gutman

Publication year - 2008

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm0801118p

Subject(s) - mathematics , integer (computer science) , combinatorics , graph , square root , eigenvalues and eigenvectors , square (algebra) , discrete mathematics , geometry , physics , computer science , programming language , quantum mechanics

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. Bapat and Pati (Bull. Kerala Math. Assoc., 1 (2004) 129-132) proved that (a) E(G) is never an odd integer. We now show that (b) E(G) is never the square root of an odd integer. Furthermore, if r and s are integers such that r ≥ 1 and 0 ≤ s ≤ r - 1 and q is an odd integer, then E(G) cannot be of the form (2s q)1/r, a result that implies both (a) and (b) as special cases.

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