TY - JOUR

T1 - Some New Bounds for the Inverse Sum Indeg Energy of Graphs

AU - Li, Fengwei

AU - Ye, Qingfang

AU - Broersma, Hajo

N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/5

Y1 - 2022/5

N2 - Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inverse sum indeg matrix of G is the n × n matrix C(G) with entries (formula presented), if the i-th and the j-th vertices are adjacent and 0 otherwise. Let µ1 ≥ µ2 ≥ … ≥ µn be the eigenvalues of C arranged in order. The inverse sum indeg energy of G, εisi (G) can be represented as ∑nj=1|µi|. In this paper, we establish several novel upper and lower sharp bounds on µ1 and εisi (G) via some other graph parameters, and describe the structures of the extremal graphs.

AB - Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inverse sum indeg matrix of G is the n × n matrix C(G) with entries (formula presented), if the i-th and the j-th vertices are adjacent and 0 otherwise. Let µ1 ≥ µ2 ≥ … ≥ µn be the eigenvalues of C arranged in order. The inverse sum indeg energy of G, εisi (G) can be represented as ∑nj=1|µi|. In this paper, we establish several novel upper and lower sharp bounds on µ1 and εisi (G) via some other graph parameters, and describe the structures of the extremal graphs.

KW - energy

KW - inverse sum indeg index

KW - ISI energy

KW - ISI matrix

UR - http://www.scopus.com/inward/record.url?scp=85131588564&partnerID=8YFLogxK

U2 - 10.3390/axioms11050243

DO - 10.3390/axioms11050243

M3 - Article

AN - SCOPUS:85131588564

SN - 2075-1680

VL - 11

JO - Axioms

JF - Axioms

IS - 5

M1 - 243

ER -