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The atom-bond connectivity index of a graph $G$ ($ABC$ index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of $G$. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the $ABC$ index among all $n$ vertex cactus graphs.
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참고문헌 (20)
참고문헌 신청
B. Ben-Moshe / 2005 / Efficient algorithms for the weighted 2-center problem in a cactus graph / 16th Int. Symp., ISAAC 2005 : 693 ~
B. Furtula / 2009 / Atom-bond connectivity index of trees / Dis-crete Appl. Math 157 (13) : 2828 ~ 2835
B. Paten / 2011 / Cactus graphs for genome comparisons / J. Comput. Biol 18 (3) : 469 ~ 481
D. B. West / 2001 / Introduction to Graph Theory / Prentice Hall
E. El-Mallah / 1988 / The complexity of some edge deletion problems / IEEE Trans. Circuits and Systems 35 (3) : 354 ~ 362
B. Furtula / 2009 / Atom-bond connectivity index of trees / Dis-crete Appl. Math 157 (13) : 2828 ~ 2835
B. Paten / 2011 / Cactus graphs for genome comparisons / J. Comput. Biol 18 (3) : 469 ~ 481
D. B. West / 2001 / Introduction to Graph Theory / Prentice Hall
E. El-Mallah / 1988 / The complexity of some edge deletion problems / IEEE Trans. Circuits and Systems 35 (3) : 354 ~ 362
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