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A363705
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The minimum irregularity of all maximal 2-degenerate graphs with n vertices.
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0
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0, 4, 2, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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3,2
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COMMENTS
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The irregularity of a graph is the sum of the differences between the degrees over all edges of the graph.
A maximal 2-degenerate graph can be constructed from a 2-clique by iteratively adding a new 2-leaf (vertex of degree 2) adjacent to two existing vertices.
This is also the minimum sigma irregularity of all maximal 2-degenerate graphs with n vertices. (The sigma irregularity of a graph is the sum of the squares of the differences between the degrees over all edges of the graph).
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LINKS
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FORMULA
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a(n) = 8 for n > 6.
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EXAMPLE
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For n=3, K_3 has irregularity 0, so a(3) = 0.
For n=4, K_4 minus an edge has irregularity 4, so a(4) = 4.
For n=5, K_4 with a subdivided edge has irregularity 2, so a(5) = 2.
For n>6, add a 2-leaf adjacent to the 2-leaves of the square of a path. This graph has irregularity 8, so a(n) = 8.
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MATHEMATICA
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PadRight[{0, 4, 2, 6}, 100, 8] (* Paolo Xausa, Nov 29 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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