Zero knowledge proof relation + number is binary
To prove "the same" relation, just use the same response of $\Sigma$-protocol for each $s_i$ in relations for $Y$, $Z$ and $s_i \in \{0,1\}$. This technique was suggested by Chaum, Evertse, de Graaf in Eurocrypt'87 paper.

To prove OR relation, one would split the challenge, prove the valid part and simulate the false one. See Cramer, Damgaard, Schoenmakers Crypto'94 paper. For preprint link and extended "CDS" description see Alan Sz' answer at Zero-knowledge proof of a product.

It may be practical to get some chapters (in pdf) of "Rethinking PKI" book  from credentica.com for both proofs. Warning: it takes time to read and understand that.

Yet another technique would be extending $\Sigma$-protocol into polinomials of degree higher than linear in challenge, see a paper in MFCS 2012. It fits well polinomial graph representation, but might be an overkill for this task.