in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

in this paper, at first we introduce a new index with the name co-pi index and obtain someproperties related this new index. then we compute this new index for tuc4c8(r) nanotubes.

in this paper, at first we mention to some results related to pi and vertex co-pi indices and then we introduce the edge versions of co-pi indices. then, we obtain some properties about these new indices.

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

In this paper, at first we mention to some results related to PI and vertex Co-PI indices and then we introduce the edge versions of Co-PI indices. Then, we obtain some properties about these new indices.

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

PI: Molly E. Cummings Integrative Biology Department University of Texas Austin, TX 78712 phone: (512) 232-6243 fax: (512) 471-3878 email: [email protected] Co-PI: Samir Ahmed (City College of New York) Co-PI: Heidi Dierssen (University of Connecticut) Co-PI: Alexander Gilerson (City College of New York) Co-PI: William F. Gilly (Stanford University) Co-PI: George Kattawar (Texas A & M...