In this paper, we obtain the vertex Padmakar-Ivan index of H-generalized join of graphs. As a consequence, we find the vertex Padmakar-Ivan index of the lexicographic product of graphs, the ideal-based zero-divisor graph and the zero-divisor graph of rings. In addition, we obtain the vertex Padmakar-Ivan index of the ideal-based zero-divisor graph and the zero-divisor graph of the ring of integers modulo n.
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Noorul Islam Ctr Higher Educ, Dept Math, Kumaracoil 629175, Tamil Nadu, IndiaNoorul Islam Ctr Higher Educ, Dept Math, Kumaracoil 629175, Tamil Nadu, India
Philipose, Roshan Sara
Balakrishnan, Sarasija Perurkada
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Noorul Islam Ctr Higher Educ, Dept Math, Kumaracoil 629175, Tamil Nadu, IndiaNoorul Islam Ctr Higher Educ, Dept Math, Kumaracoil 629175, Tamil Nadu, India