Abstract
Let G be a simple graph of order n and A be its adjacency matrix. Let Ī» 1 ā„ Ī» 2 ā„ ā¦ ā„ Ī» n be eigenvalues of matrix A . Then, the energy of a graph G is defined as Īµ G = ā i = 1 n Ī» i . In this paper, we will discuss the new lower bounds for the energy of nonsingular graphs in terms of degree sequence, 2-sequence, the first Zagreb index, and chromatic number. Moreover, we improve some previous well-known bounds for connected nonsingular graphs.
Highlights
We assume that G is a simple graph and that V(G) and E(G) are the vertex set and the edge set so that |V(G)| n and |E(G)| m
Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called vertex coloring. e smallest number of colors needed to color a graph G is called its chromatic number of G, denoted by Ļ(G)
E sum of the degrees of the vertices adjacent to vi is call the 2-degree of vi and denoted by hi. e average degree is 2 degree, and we denote by hi/di the average degree of vi. e first Zagreb of G, introduced in [1], is defined as follows: M1(G) ō½ d2vi
Summary
We assume that G is a simple graph and that V(G) and E(G) are the vertex set and the edge set so that |V(G)| n and |E(G)| m. Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called vertex coloring. According to the eigenvalues of the adjacency matrix, the energy of a graph is defined as follows: Īµ(G). Filipovski and Jajcay [5], derived some of the bounds for the energy. In 2020, Filipovski and Jajcay [5] derived some of lower bounds for the energy. In 2021, Filipovski and Jajcay [5] obtained new bounds for the energy. We continue this discussion by obtaining new bounds for the energy of nonsingular connected graph and improving some important bounds.
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