3 problems

Let $P$ be a finite set in $\mathbb{R}^m$, and let $E_2(P)$ denote its second distance energy, namely the number of ordered quadruples $(a,b,c,d)\in P^4$ satisfying $|a-b|=|c-d|$.…

Let $G$ be a clique tree of order $n$ whose cliques are $K_{n_1},\ldots,K_{n_k}$. For a clique path $\mathbb{P}_{m_1,\ldots,m_k}$, let $\mathbb{P}_{m_1,\ldots,m_k}$ denote the grap…

Let $G$ be a connected graph on $n$ vertices, and let $DE(G)$ denote its distance energy. Ramane et al.'s conjecture. Among all connected graphs on $n$ vertices, the complete graph…