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              <text>Transitivity of trees</text>
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              <text>domatic number; Domination; transitivity</text>
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              <text>For a graph G = (V,E), a partition ? = (V1,V2,..,Vk) of the vertex set V is a transitive partition if Vi dominates Vj whenever i &amp;lt; j. The transitivity Tr(G) of a graph G is the maximum order of a transitive partition of V. For any positive integer k, we characterize the smallest tree with transitivity k and obtain an algorithm to determine the transitivity of any tree of finite order.   2022 World Scientific Publishing Company.</text>
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              <text>Samuel L.C.; Joseph M.</text>
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              <text>Discrete Mathematics, Algorithms and Applications, Vol-14, No. 6</text>
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              <text>&lt;a href="https://doi.org/10.1142/S1793830922500203" target="_blank" rel="noreferrer noopener"&gt;https://doi.org/10.1142/S1793830922500203&lt;/a&gt;
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              <text>ISSN: 17938309</text>
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              <text>Samuel L.C., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, India; Joseph M., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, India</text>
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