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Abstract
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The distance d(u, v) between the vertices u and v of a connected graph G is defined
as the number of edges in a minimal path connecting them. The transmission of a vertex
v of G is defined by s(v) = A
u2V(G)
d(v, u). In this article we aim to define some
transmission-based topological indices. We obtain lower and upper bounds on these
indices and characterize graphs for which these bounds are best possible. Finally, we
find these indices for various graphs using the group of automorphisms of G. This is an
efficient method of finding these indices especially when the automorphism group of G
has a few orbits on V(G) or E(G).
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