Theorem 9
For a complete graph \((K_n)_S\) with \(\sigma\) self-loops,
$$\begin{aligned} E_{ABC}(K_n)_S=(n-\sigma -1)\left( \frac{\sqrt{2n-4}}{n-1}\right) +(n-2)\left( \frac{\sigma \sqrt{2n}}{n(n+1)}\right)…

For a complete graph \((K_n)_S\) with \(\sigma\) self-loops,
$$\begin{aligned} E_{ABC}(K_n)_S=(n-\sigma -1)\left( \frac{\sqrt{2n-4}}{n-1}\right) +(n-2)\left( \frac{\sigma \sqrt{2n}}{n(n+1)}\right)…

Let \({\mathcalligra{w}}_{1} = \left( { \eta_{{{\mathcalligra{w}}_{1} }} , \xi_{{{\mathcalligra{w}}_{1} }} } \right)\) and \({\mathcalligra{w}}_{2} = \left( { \eta_{{{\mathcalligra{w}}_{2} }} ,…

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