Yes, that's what I wanted (the multi-city search in graph). But thanks anyway. I'll try to find other ways.

Right now (at least when I checked yesterday), the lowest-priced airline for your dates, flying from LAX, was American Airlines, for reasonable flights with one stop in each direction (I didn't check which airport is the stop). If you check for a round-trip flight to and from Barcelona, which I did before switching to "multi-city", then British Airlines comes up the cheapest. You might just check these two airlines' websites fo rmore detail. I find BA easy to use and they do show prices for every day of a week, with your chosen date in the middle. I imagine AA has a similar multi-day search option, but I've not used them.

For any airline, make sure you get the complete price with taxes added on. BA taxes are high, but I assume the price on Kayak includes those.

In my experience, Kayak's quoted prices are all-inclusive (fare + taxes + fees). One reason I like them so much!