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A372026
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Minimum second Zagreb index of maximal 2-degenerate graphs with n vertices.
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4
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12, 33, 51, 86, 116, 147, 178, 210, 242, 274, 306, 338, 370, 402, 434, 466, 498, 530, 562, 594, 626, 658, 690, 722, 754, 786, 818, 850, 882, 914, 946, 978, 1010, 1042, 1074, 1106, 1138, 1170, 1202, 1234, 1266, 1298, 1330, 1362, 1394, 1426, 1458, 1490, 1522, 1554, 1586, 1618, 1650, 1682, 1714, 1746, 1778, 1810
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OFFSET
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3,1
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COMMENTS
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The second Zagreb index of a graph is the sum of the products of 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. The extremal graphs are described in (Bickle 2024).
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LINKS
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FORMULA
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a(n) = 32*n-110 for n>8.
a(n) = 2*a(n-1) - a(n-2) for n > 10.
G.f.: x^3*(x^7 + x^5 - 5*x^4 + 17*x^3 - 3*x^2 + 9*x + 12)/(x - 1)^2. (End)
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EXAMPLE
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The graph K_3 has 3 degree 2 vertices, so a(3) = 3*4 = 12.
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CROSSREFS
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Cf. A372027 (second Zagreb index of MOPs).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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