[PDF][PDF] A lower bound for graph energy in terms of minimum and maximum degrees
S Akbari, M Ghahremani… - … Math. Comput. Chem, 2021 - match.pmf.kg.ac.rs
MATCH Commun. Math. Comput. Chem, 2021•match.pmf.kg.ac.rs
The energy of a graph G, denoted by E (G), is defined as the sum of absolute values of all
eigenvalues of G. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631–633) it was
conjectured that for every graph G with maximum degree∆(G) and minimum degree δ (G)
whose adjacency matrix is non-singular, E (G)≥∆(G)+ δ (G) and the equality holds if and
only if G is a complete graph. Here, we prove the validity of this conjecture for planar graphs,
triangle-free graphs and quadrangle-free graphs.
eigenvalues of G. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631–633) it was
conjectured that for every graph G with maximum degree∆(G) and minimum degree δ (G)
whose adjacency matrix is non-singular, E (G)≥∆(G)+ δ (G) and the equality holds if and
only if G is a complete graph. Here, we prove the validity of this conjecture for planar graphs,
triangle-free graphs and quadrangle-free graphs.
Abstract
The energy of a graph G, denoted by E (G), is defined as the sum of absolute values of all eigenvalues of G. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631–633) it was conjectured that for every graph G with maximum degree∆(G) and minimum degree δ (G) whose adjacency matrix is non-singular, E (G)≥∆(G)+ δ (G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for planar graphs, triangle-free graphs and quadrangle-free graphs.
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