WIENER POLYNOMIALS AND WIENER INDICES OF THE TRANSFORMATION GRAPHS
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Topological graph indices are proven to be one of the most useful mathematical tools in the study of graphs, especially molecular graphs. Probably the most famous one is the Wiener index which was primarily used in determining the boiling points of the isomers of alkane molecules. The Wiener polynomial of G, denoted by W(G; q) is de ned by W(G; q) = P fu;vgV (G) qd(u;v) where d(u; v) is the distance between the vertices u and v. The Wiener index W(G), a distance based graph invariant, is given by W(G) = P fu;vgV (G) d(u; v). In this paper, mo- tivated by the above facts, the Wiener polynomial and Wiener index of transformation graph G+++ are determined when G is isomorphic to Pn; Cn; K1;n; Kn; Wn+1, the comb and nally the tadpole graph. We have also determined the Wiener polynomial and Wiener index of trans- formation graphs Gxyz of G when G isomorphic to Pn and Cn. Finally, the formula for W(G++; q) is given.
Abstract
Topological graph indices are proven to be one of the most useful mathematical tools in the study of graphs, especially molecular graphs. Probably the most famous one is the Wiener index which was primarily used in determining the boiling points of the isomers of alkane molecules. The Wiener polynomial of G, denoted by W(G; q) is de ned by W(G; q) = P fu;vgV (G) qd(u;v) where d(u; v) is the distance between the vertices u and v. The Wiener index W(G), a distance based graph invariant, is given by W(G) = P fu;vgV (G) d(u; v). In this paper, mo- tivated by the above facts, the Wiener polynomial and Wiener index of transformation graph G+++ are determined when G is isomorphic to Pn; Cn; K1;n; Kn; Wn+1, the comb and nally the tadpole graph. We have also determined the Wiener polynomial and Wiener index of trans- formation graphs Gxyz of G when G isomorphic to Pn and Cn. Finally, the formula for W(G++; q) is given.
참고문헌 (8)
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