PRODUCTG(1)

💖 PRODUCTG 💖

okay bestie, gather round, because today we're talking about productg — yes, that's the manual page for productg 2.9.3, and it is lowkey iconic. 🫶

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✨ SYNOPSIS ✨

productg [-u|-c|-l|-L|-k|-t|-a#] [infile [outfile]]

that's it. that's the whole vibe. one tool, two graphs, infinite slay. 👑

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🌸 DESCRIPTION 🌸

so here's the tea: productg reads two graphs in graph6/sparse6 format and writes their product — either in sparse6 or dreadnaut format. two graphs go in, one gloriously multiplied graph comes out. the way that works?? math. 💅

and if you want to pick which kind of product, that's what the flags are for, bestie. every single one of them, coming right up:

• -d — Dreadnaut format. (the default is sparse6, so only reach for this if you want the other flavour.) 🦋
• -c — Cartesian product. ✨
• -l — Lexicographic product, written as G1[G2]. 🎀
• -L — Lexicographic product, written as G2[G1]. (yeah, same product family, flipped order — capital L is the plot twist.) 🌀
• -t — Tensor product. also known as the Kronecker, categorical, or direct product. so many names for one little guy, we love a multi-hyphenate. 🔥
• -k — Complete product. also goes by strong or normal product. 👑
• -a# — the general case, where the argument is a 3-digit octal number. this is the build-your-own-product option and honestly? main character energy.
• -u — Disjoint union. 🧚
• -q — Suppress informative output. for when you want it to be quiet and mysterious. 🙈

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🌈 the -a# deep dive (iykyk)

okay so for -a# you add these values together and that sum gives you the condition for an edge. each digit position is a little vibe check between the two graphs, fr fr:

• 400 — Graph1: same, Graph2: same
• 200 — Graph1: same, Graph2: adj
• 100 — Graph1: same, Graph2: nonadj
• 040 — Graph1: adj, Graph2: same
• 020 — Graph1: adj, Graph2: adj
• 010 — Graph1: adj, Graph2: nonadj
• 004 — Graph1: nonadj, Graph2: same
• 002 — Graph1: nonadj, Graph2: adj
• 001 — Graph1: nonadj, Graph2: nonadj

and the codes line up like this, in order, so you can literally just read across:

Code:    400   200   100   040   020   010   004   002   001
Graph1:  same  same  same  adj   adj   adj   nonadj nonadj nonadj
Graph2:  same  adj   nonadj same  adj   nonadj same  adj   nonadj

ngl bestie, don't guess at these — add the values you actually want and let the octal digits do the talking. the table above is the whole map. 🗺️

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and that's the page!! productg version 2.9.3, from September 2026, out here in the User Commands section being absolutely everything. go multiply some graphs, bestie. periodt. 💜🌸✨