{
  "id": "2207.04599",
  "version": "v1",
  "published": "2022-07-11T03:10:49.000Z",
  "updated": "2022-07-11T03:10:49.000Z",
  "title": "A lower bound of the energy of non-singular graphs in terms of average degree",
  "authors": [
    "Saieed Akbari",
    "Hossein Dabirian",
    "S. Mahmood Ghasemi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph of order $n$ with adjacency matrix $A(G)$. The \\textit{energy} of graph $G$, denoted by $\\mathcal{E}(G)$, is defined as the sum of absolute value of eigenvalues of $A(G)$. It was conjectured that if $A(G)$ is non-singular, then $\\mathcal{E}(G)\\geq\\Delta(G)+\\delta(G)$. In this paper we propose a stronger conjecture as for $n \\geq 5$, $\\mathcal{E}(G)\\geq n-1+ d$, where $d$ is the average degree of $G$. Here, we show that conjecture holds for bipartite graphs, planar graphs and for the graphs with $d \\leq n-2\\ln n -3$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-11T03:10:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average degree",
      "lower bound",
      "non-singular graphs",
      "bipartite graphs",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}