On Trees with Given Independence Numbers with Maximum Gourava Indices

In mathematical chemistry, molecular descriptors serve an important role, primarily in quantitative structure–property relationship (QSPR) and structure–activity (QSAR) studies. A topological index of a graph is real number that invariant under isomorphism conditions provides information about its size, symmetry, degree branching, cyclicity. For any N, the first second Gourava indices are defined as GO1(N)=∑u′v′∈E(N)(d(u′)+d(v′)+d(u′)d(v′)) GO2(N)=∑u′v′∈E(N)(d(u′)+d(v′))d(u′)d(v′), respectively.The independence being cardinality maximal independent set, plays vital role reading energies chemical trees. this research paper, it shown among family trees order δ ξ, spur tree denoted Υδ,ξ maximizes both 1st 2nd indices, with these characterizations unique.