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http://dx.doi.org/10.11568/kjm.2015.23.3.401

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)
Publication Information
Korean Journal of Mathematics / v.23, no.3, 2015 , pp. 401-408 More about this Journal
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.
Keywords
k-apex tree; First Zagreb index; Second Zagreb index;
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