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Relations between ordinary and multiplicative degree-based topological indices
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Let G be a simple connected graph with n vertices and m edges, and sequence
of vertex degrees d1 ? d2 ?...? dn > 0. If vertices i and j are
adjacent, we write i ~ j. Denote by ?1, ?*1, Q? and H? the multiplicative
Zagreb index, multiplicative sum Zagreb index, general first Zagreb index,
and general sumconnectivity index, respectively. These indices are defined
as ?1 = ?ni=1 d2i, ?*1 = ?i~j(di+dj), Q? = ?n,i=1 d?i and H? = ?i~j(di+dj)?. We establish upper and lower bounds for the differences H?-m (?1*)?/m and Q?-n(?1)?/2n . In this way we generalize a number of
results that were earlier reported in the literature.
Title: Relations between ordinary and multiplicative degree-based topological indices
Description:
Let G be a simple connected graph with n vertices and m edges, and sequence
of vertex degrees d1 ? d2 ?.
? dn > 0.
If vertices i and j are
adjacent, we write i ~ j.
Denote by ?1, ?*1, Q? and H? the multiplicative
Zagreb index, multiplicative sum Zagreb index, general first Zagreb index,
and general sumconnectivity index, respectively.
These indices are defined
as ?1 = ?ni=1 d2i, ?*1 = ?i~j(di+dj), Q? = ?n,i=1 d?i and H? = ?i~j(di+dj)?.
We establish upper and lower bounds for the differences H?-m (?1*)?/m and Q?-n(?1)?/2n .
In this way we generalize a number of
results that were earlier reported in the literature.
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