TY - JOUR
ID - 113971
TI - Deficiency Sum Energy of Some Graph Classes
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Singh, Omendra
AU - Garg, Pravin
AU - Kansal, Neha
AD - Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
Y1 - 2023
PY - 2023
VL - 14
IS - 3
SP - 145
EP - 160
KW - Deficiency sum matrix
KW - Deficiency sum energy
KW - Deficiency sum eigenvalues
KW - Deficiency
DO - 10.22052/ijmc.2023.252633.1698
N2 - 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 $G$.
UR - https://ijmc.kashanu.ac.ir/article_113971.html
L1 - https://ijmc.kashanu.ac.ir/article_113971_6a0f0a71de5939bc3635ff1461755abd.pdf
ER -