The Euler Sombor index of a graph

Abstract

AbstractA novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors, which is the perimeter of an ellipse whose focal points represent the degree‐point and its dual‐point of a pair of adjacent vertices in a graph . We first analyze the chemical applicability of this elliptic Sombor index, and then establish its mathematical properties and determine the extremal values for this elliptic Sombor index among all (molecular) trees and characterize the corresponding extremal graphs.