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Some results on dominating induced matchings

Akbari, S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-022-02470-6
  3. Publisher: Springer Japan , 2022
  4. Abstract:
  5. Let G be a graph, a dominating induced matching (DIM) of G is an induced matching that dominates every edge of G. In this paper we show that if a graph G has a DIM, then χ(G) ≤ 3. Also, it is shown that if G is a connected graph whose all edges can be partitioned into DIM, then G is either a regular graph or a biregular graph and indeed we characterize all graphs whose edge set can be partitioned into DIM. Also, we prove that if G is an r-regular graph of order n whose edges can be partitioned into DIM, then n is divisible by (2r-1r-1) and n=(2r-1r-1) if and only if G is the Kneser graph with parameters r- 1 , 2 r- 1. © 2022, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature
  6. Keywords:
  7. Dominating induced matching ; Induced matching ; Kneser graph
  8. Source: Graphs and Combinatorics ; Volume 38, Issue 3 , 2022 ; 09110119 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00373-022-02470-6