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the number of 1-nearly independent edge subsets
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نویسنده
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andriantiana eric o. d. ,shozi zekhaya b.
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منبع
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iranian journal of mathematical chemistry - 2025 - دوره : 16 - شماره : 1 - صفحه:65 -84
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چکیده
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let $g=(v(g),e(g))$ be a graph with the set of vertices $v(g)$ and the set of edges $e(g)$. a subset $s$ of $e(g)$ is called a $k$-nearly independent edge subset if there are exactly $k$ pairs of elements of $s$ that share a common end. $z_k(g)$ is the number of such subsets.this paper studies $z_1$. various properties of $z_1$ are discussed. we characterize the two $n$-vertex trees with the smallest $z_1$, as well as the one with the largest value. a conjecture on the $n$-vertex tree with the second-largest $z_1$ is proposed.
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کلیدواژه
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1-nearly independent edge subset ,minimal graphs ,maximal graphs
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آدرس
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rhodes university, department of mathematics (pure and applied), south africa, university of kwazulu-natal, school of mathematics, statistics and computer science, south africa
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پست الکترونیکی
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zekhaya@aims.ac.za
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Authors
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