TY - JOUR

T1 - Inverse Sum Indeg Index (Energy) with Applications to Anticancer Drugs

AU - Altassan, Alaa

AU - Rather, Bilal Ahmad

AU - Imran, Muhammad

N1 - Funding Information:
This research work was funded by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia under grant no. (IFPIP: 309-247-1443). The authors gratefully acknowledge the technical and financial support provided by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.
Publisher Copyright:
© 2022 by the authors.

PY - 2022/12

Y1 - 2022/12

N2 - For a simple graph with vertex set (Formula presented.) with degree sequence (Formula presented.) of vertex (Formula presented.), the inverse sum indeg matrix ((Formula presented.) -matrix) (Formula presented.) of G is defined by (Formula presented.) if (Formula presented.) is adjacent to (Formula presented.), and zero, otherwise. The multiset of eigenvalues of (Formula presented.) is the (Formula presented.) -spectrum of G and the sum of their absolute values is the (Formula presented.) -energy of (Formula presented.). In this paper, we modify the two results of (Li, Ye and Broersma, 2022), give the correct characterization of the extremal graphs and thereby obtain better bounds than the already known results. Moreover, we also discuss the QSPR analysis and carry the statistical modelling (linear, logarithmic and quadratic) of the physicochemical properties of anticancer drugs with the (Formula presented.) -index (energy).

AB - For a simple graph with vertex set (Formula presented.) with degree sequence (Formula presented.) of vertex (Formula presented.), the inverse sum indeg matrix ((Formula presented.) -matrix) (Formula presented.) of G is defined by (Formula presented.) if (Formula presented.) is adjacent to (Formula presented.), and zero, otherwise. The multiset of eigenvalues of (Formula presented.) is the (Formula presented.) -spectrum of G and the sum of their absolute values is the (Formula presented.) -energy of (Formula presented.). In this paper, we modify the two results of (Li, Ye and Broersma, 2022), give the correct characterization of the extremal graphs and thereby obtain better bounds than the already known results. Moreover, we also discuss the QSPR analysis and carry the statistical modelling (linear, logarithmic and quadratic) of the physicochemical properties of anticancer drugs with the (Formula presented.) -index (energy).

KW - ISI-matrix

KW - adjacency matrix

KW - anticancer drugs

KW - correlation

KW - topological indices

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U2 - 10.3390/math10244749

DO - 10.3390/math10244749

M3 - Article

AN - SCOPUS:85144649030

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 24

M1 - 4749

ER -