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A strict inequality on the energy of edge partitioning of graphs

Akbari, S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2022.2083055
  3. Publisher: Taylor and Francis Ltd , 2022
  4. Abstract:
  5. Let G be a graph. The energy of G, (Formula presented.), is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and (Formula presented.) is an edge partition of G, such that (Formula presented.) are spanning; then (Formula presented.) if and only if (Formula presented.), for every (Formula presented.) and (Formula presented.), where (Formula presented.) is the adjacency matrix of (Formula presented.). It was proved that if G is a graph and (Formula presented.) are subgraphs of G which partition edges of G, then (Formula presented.). In this paper we show that if G is connected, then the equality is strict, that is (Formula presented.). © 2022 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Edge partition ; Energy of graph
  8. Source: Linear and Multilinear Algebra ; 2022 ; 03081087 (ISSN)
  9. URL: https://www.tandfonline.com/doi/full/10.1080/03081087.2022.2083055