Deficiency Sum Energy of Some Graph Classes

Document Type : Research Paper


Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India


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 $G$‎.


Main Subjects

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