Say I have a graph G and I want to sum some constant C (like the minimum degree of the graph) for every vertex. Can I use the following notation? $$\sum_{x \in V(G)}C $$

Is this an appropriate way to use sigma notation? There is a similar question here Notation of the summation of a set of numbers but it doesn't account for the fact that the expression could be a constant. A person I am working with questioned it and I couldn't find any resources where it is used in this manner. I don't see why it would be improper because you could have an expression like $\sum_{i=1}^{n}C$. Thank you

  • $\begingroup$ It looks logically correct, but why wouldn't you just write $\lvert V(G)\rvert \cdot C$? $\endgroup$ – David K Dec 6 '18 at 22:03
  • $\begingroup$ We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted. $\endgroup$ – rachelhoward Dec 6 '18 at 22:09
  • $\begingroup$ OK, I could imagine your notation as an intermediate step while simplifying some other sum where you can separate out a constant term. Some authors would skip that intermediate step and go straight to the the multiplication but I think that is something you can decide not do to if you think it's helpful to show the intermediate step explicitly. $\endgroup$ – David K Dec 6 '18 at 22:16

Indeed, you are correct, you can use $\sum_{x \in S} C$ for any set $S$ and constant $C$, and since $C$ does not depend on $x$, this simplifies to $$ \sum_{x \in S} C = C \cdot |S|, $$ for any finite set $S$.


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