Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MAXIMUM ZAGREB INDICES IN THE CLASS OF k-APEX TREES

  • SELENGE, TSEND-AYUSH (Department of Mathematics National University of Mongolia, Department of Mathematics Sungkyunkwan University) ;
  • HOROLDAGVA, BATMEND (Department of Mathematics Mongolian National University of Education, Department of Mathematics Sungkyunkwan University)
  • Received : 2015.08.10
  • Accepted : 2015.09.07
  • Published : 2015.09.30
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Abstract

The first and second Zagreb indices of a graph G are defined as $M_1(G)={\sum}_{{\nu}{\in}V}d_G({\nu})^2$ and $M_2(G)={\sum}_{u{\nu}{\in}E(G)}d_G(u)d_G({\nu})$. where $d_G({\nu})$ is the degree of the vertex ${\nu}$. G is called a k-apex tree if k is the smallest integer for which there exists a subset X of V (G) such that ${\mid}X{\mid}$ = k and G-X is a tree. In this paper, we determine the maximum Zagreb indices in the class of all k-apex trees of order n and characterize the corresponding extremal graphs.

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