Extremal graphs with respect to modified Sombor index

The modified Sombor (mSO) index of a given graph [Formula: see text] is symbolized with mSO and define by sum of the weights [Formula: see text], where [Formula: see text] is the degree of a vertex [Formula: see text] in [Formula: see text]. In this work, we present the first and second maximum values of the mSO index among all [Formula: see text]-vertex [Formula: see text]-cyclic graphs. We also provide that the mSO index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the mSO index of connected chemical graphs.