Deficiency Sum Energy of Some Graph Classes
نویسندگان
1 Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
2 Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
3 Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
doi
10.22052/ijmc.2023.252633.1698چکیده
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 $G$.
