The Zagreb indices have been introduced by Gutman and Trinajstić as M1(G) = v∈V (G) (dG(v)) 2 and M2(G) = uv∈E(G) dG(u)dG(v), where dG(u) denotes the degree of vertex u. We now define a new version of Zagreb indices as M * 1 (G) = uv∈E(G) [εG(u) + εG(v)] and M * 2 (G) = uv∈E(G) εG(u)εG(v), where εG(u) is the largest distance between u and any other vertex v of G. The goal of this paper is to further the study of these new topological index.
The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. In this paper, the vertex PI and Szeged indices of an infinite family of fullerenes are computed.
A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number (gp-number) gp(G) of G. The gp-number is determined for some families of Kneser graphs, in particular for K(n, 2) and K(n, 3). A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.
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