The Seidel energy minimization conjecture for chain graphs

Let $G$ be a chain graph of order $n$ with binary string

$$b=0^{s_1}1^{t_1}0^{s_2}\ldots 0^{s_k}1^{t_k},$$

where

$$\sum_{i=1}^k(s_i+t_i)=n,$$

and $s_i\geq 1$ and $t_i\geq 1$ for $1\leq i\leq k$. Let $SE(G)$ denote the Seidel energy, and let $H\in\Gamma_{n,k}$. Seidel energy minimization conjecture.

$$SE(G)\geq SE(H).$$

Moreover, equality holds if and only if $G\in\Gamma_{n,k}$. This conjecture proposes that the graphs in $\Gamma_{n,k}$ minimize Seidel energy among the specified chain graphs, with equality characterized precisely by membership in $\Gamma_{n,k}$; its resolution is not indicated in the supplied text.