Spectral radius and energy of Sombor matrix of graphs


Zhao Wang, Yaping Mao, Ivan Gutman, Jichang Wu, Qin Ma




Let G be a graph of order n. For i = 1, 2,. .. , n, let d i be the degree of the vertex v i of G. The Sombor matrix A so of G is defined so that its (i, j)-entry is equal to d 2 i + d 2 j if the vertices v i and v j are adjacent, and 0 otherwise. The spectral radius η 1 and the energy E so of A so are examined. In particular, upper bounds on E so are obtained, as well as Nordhaus–Gaddum–type results for η 1 and E so .