Extremal Polyomino Chains of VDB Topological Indices
نویسندگان
چکیده
We show that the zig-zag chain Z3 n of segments of length 3 (see Figure 2) has the minimal ABC index among all polyomino chains with n squares. More generally, we give conditions on the numbers {φij} under which the zig-zag chain Z3 n is an extremal value of the induced topological index T defined by T (G) = ∑ 1≤i≤j≤n−1 mijφij where G is a graph with n vertices and mij is the number of edges of G with terminal vertices of degree i and j. We also find extremal values of the general Randić index Rα over the set of all polyomino chains, for some values of α. Mathematics Subject Classification: 05C76, 05C07, 05C35, 05C90
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