@article {
author = {Singh, Omendra and Garg, Pravin and Kansal, Neha},
title = {Deficiency Sum Energy of Some Graph Classes},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {14},
number = {3},
pages = {145-160},
year = {2023},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2023.252633.1698},
abstract = {In this paper, we introduce the concept of deficiency sum matrix $S_{df}(G)$ of a simple graph $G=(V,E)$ of order $n$. The deficiency $df(v)$ of a vertex $v \in V$ is the deviation between the degree of the vertex $v$ and the maximum degree of the graph. The deficiency sum matrix $S_{df}(G)$ is a matrix of order $n$ whose $(i,j)$-th entry is $df(v_{i})+df(v_{j})$, if the vertices $v_{i}$ and $v_{j}$ are adjacent and $0$, otherwise. In addition, we introduce deficiency sum energy $ES_{df}(G)$ of a graph $G$ and establish some bounds for $ES_{df}(G)$. Further, deficiency sum energy of some classes of graphs are obtained. Moreover, we construct an algorithm and python(3.8) code to find out spectrum and deficiency sum energy of graph $G$.},
keywords = {Deficiency sum matrix,Deficiency sum energy,Deficiency sum eigenvalues,Deficiency},
url = {https://ijmc.kashanu.ac.ir/article_113971.html},
eprint = {https://ijmc.kashanu.ac.ir/article_113971_6a0f0a71de5939bc3635ff1461755abd.pdf}
}