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Let α 2 denote the proportion of quadratic sum of P b P T f in the quadratic sum of graph signal f.
where α 1 denote the proportion of quadratic sum of graph signals associated with sampled vertices in the quadratic sum of graph signals associated with all the vertices, i.e., begin{array}rcl@ {alpha_{1}} = frac{{sumlimits_{u in S} {{{left| {fleft u right)} right|}^{2}}} }}{{sumlimits_{v in V} {{{left| {fleft(v right)} right|}^{2}}} }} end{array}.
The TRA measure is defined as the weighted sum of graph operations, normalized by the number of markers (i.e. by the number of nodes in the reference graph) to facilitate the comparison between videos (datasets) with different numbers of cells.
In the following lemma, we compute the size of F-sum of graphs for (F=Q).
In the following lemma, we compute the size of F-sum of graphs for (F=R).
In the following lemma, we compute the size of F-sum of graphs for (F=T).
In the following lemma, we compute the size of F-sum of graphs for (F=S).
To avoid computational complications, it is important to express the formulas for the product of F-sum of graphs in terms of their factor graphs.
We determine the lower and upper bounds for the F-index and the Narumi-Katayama index of the Cartesian product of F-sum of graphs in terms of their factor graphs for (F=S).
We determine the lower and upper bounds for the F-index and the Narumi-Katayama index of the Cartesian product of F-sum of graphs in terms of their factor graphs for (F=S) and (F=R).
We determine the lower and upper bounds for the F-index and the Narumi-Katayama index of the Cartesian product of F-sum of graphs in terms of their factor graphs for (F=R).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com