On Diameter, Cyclomatic Number and Inverse Degree of Chemical Graphs
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Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = Pni=11degG(vi). The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.
Abstract
Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = Pni=11degG(vi). The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.
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