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 - https://www.scopus.com/pages/publications/85131588564
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 -