27 citations · 33 across the 18 of their papers we have counts for
7 papers · 1 filter
The -Conjecture for CIS -Graphs
Yinchen Liu, Quanyu Tang
We prove the -conjecture, which dates back to Gurvich's 1978 thesis. Specifically, let the edges of a complete graph be colored with colors , and for each let $G…
A positive square-energy strengthening of Turán's theorem
Yinchen Liu, Quanyu Tang, Shengtong Zhang
Let be an -vertex graph with clique number , and let denote the sum of the squared positive adjacency eigenvalues. We prove that $$ \sqrt{s^+(G)}\le\left(1-\f…
The positive and negative square-energy conjecture
Yinchen Liu, Quanyu Tang, Shengtong Zhang
Let and denote the sums of the squares of the positive and negative adjacency eigenvalues of a graph , respectively. We prove the conjecture of Elphick, Farber…
Path-Minimality of -Energy for Connected Graphs
Yinchen Liu, Quanyu Tang
Let be a simple connected graph on vertices, and let be the eigenvalues of its adjacency matrix . For , define the -energy of $G…
Path-Minimality for Positive -Energies, Laplacian-Type Spectra, and Line Graphs
Yinchen Liu, Quanyu Tang
We derive several applications of the path-minimality theorem for adjacency -energy proved in the companion paper. First, we prove the sharp inequality $$ \mathcal E_p^+(G)\ge \…
On a conjecture of Nikiforov concerning the minimal -energy of connected graphs
Quanyu Tang, Yinchen Liu, Wei Wang
For a given simple graph \( G \), the \( p \)-energy of \( G \), denoted by \( \mathcal{E}_p(G) \), is defined as the sum of the \( p \)-th power of the absolute values of the eige…
On the Positive and Negative -Energies of Graphs under Edge Addition
Quanyu Tang, Yinchen Liu, Wei Wang
In this paper, we introduce the concepts of positive and negative -energies of graphs and investigate their behavior under edge addition. Specifically, we generalize the classic…