Journal of applied mathematics & informatics

  • 제42권3호
  • /
  • Pages.511-520
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  • 2024
  • /
  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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THE SPLIT AND NON-SPLIT TREE (D, C)-NUMBER OF A GRAPH

  • P.A. SAFEER (Department of Mathematics, University College) ;
  • A. SADIQUALI (Department of Mathematical Sciences, M. E. A. Engineering College) ;
  • K.R. SANTHOSH KUMAR (Department of Mathematics, University College)
  • 투고 : 2023.05.24
  • 심사 : 2024.03.19
  • 발행 : 2024.05.30
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초록

In this paper, we introduce the concept of split and non-split tree (D, C)- set of a connected graph G and its associated color variable, namely split tree (D, C) number and non-split tree (D, C) number of G. A subset S ⊆ V of vertices in G is said to be a split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is disconnected. The minimum size of the split tree (D, C) set of G is the split tree (D, C) number of G, γχST (G) = min{|S| : S is a split tree (D, C) set}. A subset S ⊆ V of vertices of G is said to be a non-split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is connected and non-split tree (D, C) number of G is γχST (G) = min{|S| : S is a non-split tree (D, C) set of G}. The split and non-split tree (D, C) number of some standard graphs and its compliments are identified.

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과제정보

The authors are thankful to the referee for the useful suggestions.

참고문헌

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