In 2009, key research on triangle-free graph indices included Li and Liu’s, "Complete solution to a conjecture on the Randic index of triangle-free graphs" in Discrete Mathematics
, which established lower bounds, and Zhou and Trinajstić's, "On a novel connectivity index" in the Journal of Mathematical Chemistry
, which introduced the sum-connectivity index. These foundational papers addressed specific index calculations for graph structures lacking three-node cycles. Detailed information is available through academic databases like ScienceDirect and Springer Link. index of triangle 2009 link
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Let's express $n$ in terms of $a$, $b$, and $c$ and simplify. We have: [n = \fracabcs(s-a)(s-b)(s-c).] Using Heron's formula, the area $K$ of the triangle is given by $K^2 = s(s-a)(s-b)(s-c)$.