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On D-equivalence class of complete bipartite graphs

Aalipour-Hafshejani, G ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. Let G be a simple graph of order n. We mean by dominating set, a set S C V(G) such that every vertex of G is either in S or adjacent to a vertex in S. The domination polynomial of G is the polynomial Σni=1 (G,i)xi where d((g,i) is the number of dominating sets of G of size i. Two graphs G and H are said to be V-equivalent, written G H, if D((G, x) = D(H, x). The D-equivalence class of G is [G] = { H H G }. Recently, the determination of D-equivalence class of a given graph, has been of interest. In this paper, it is shown that for n ≥ 3, [Kn, n] has size two. We conjecture that the complete bipartite graph Km,n for n - m ≥ 2, is uniquely determined by its domination polynomial
  4. Keywords:
  5. Dominating set ; Domination polynomial
  6. Source: Ars Combinatoria ; Vol. 117, issue , Oct , 2014 , p. 275-288 ; 03817032
  7. URL: http://math.ipm.ac.ir/papers.jsp?school=Mathematics&Pfirst=811&p=status!=%27In%20Proceedings%27%20and%20status!=%27In%20Handbooks%27%20and%20status!=%27books%27%20and