# Sigma notation for iterating through number of members of a set with constant expression

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

• It looks logically correct, but why wouldn't you just write $\lvert V(G)\rvert \cdot C$? – David K Dec 6 '18 at 22:03
• We do at some point in our proof. We actually use this notation and the equation that @gt6989b posted. – rachelhoward Dec 6 '18 at 22:09
• 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. – 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 $$S$$.