Extremal hexagonal chains concerning k-matchings and k-independent sets |
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| Authors: | Lian-zhu Zhang Fu-ji Zhang |
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| Institution: | (1) Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian, 363000, China;(2) Department of Mathematics, Xiamen University, Xiamen, Fujian, 361005, China |
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| Abstract: | Denote by 
n
the set of the hexagonal chains with n hexagons. For any B
n
n
, let m
k
(B
n
) and i
k
(B
n
) be the numbers of k-matchings and k-independent sets of B
n
, respectively. In the paper, we show that for any hexagonal chain B
n
n
and for any k 0, m
k
(L
n
) m
k
(B
n
)m
k
(Z
n
) and i
k
(L
n
)i
k
(B
n
)i
k
(Z
n
), with left equalities holding for all k only if B
n
=L
n
, and the right equalities holding for all k only if B
n
=Z
n
, where L
n
and Z
n
are the linear chain and the zig-zag chain, respectively. These generalize some related results known before. |
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| Keywords: | hexagonal chain graph invariants benzenoid hydrocarbons k-matching k-independent set |
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