Extremal t‐apex trees with respect to matching energy |
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| Authors: | Kexiang Xu Zhiqing Zheng Kinkar Ch Das |
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| Institution: | 1. Department of Mathematics, College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu, People's Republic of China;2. Department of Mathematics, Sungkyunkwan University, Suwon, Republic of Korea |
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| Abstract: | The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. For any integer t≥1, a graph G is called t‐apex tree if there exists a t‐set  such that G ? X is a tree, while for any  with  , G ? Y is not a tree. Let  be the set of t‐apex trees of order n. In this article, we determine the extremal graphs from  with minimal and maximal matching energies, respectively. Moreover, as an application, the extremal cacti of order n and with s cycles have been completely characterized at which the minimal matching energy are attained. © 2015 Wiley Periodicals, Inc. Complexity 21: 238–247, 2016 |
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| Keywords: | t‐apex tree matching energy quasi‐order cactus |
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