Local antimagic chromatic number of even-by-odd flower-bouquet graphs

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Let rr and ss be integers, with rr even and r≥2r\ge 2, and ss odd and s≥3s\ge 3. Let rFB(s)rFB(s) denote the corresponding flower-bouquet graph, and let χla(G)\chi_{la}(G) be the local antimagic chromatic number of a graph GG. The even-by-odd flower-bouquet conjecture.

χla(rFB(s))=3.\chi_{la}(rFB(s))=3.

The paper proves the analogous equality for odd r,s≥3r,s\ge 3, while the even-rr, odd-ss case is posed as an open problem.

References

Primary source

Gee-Choon Lau, Wai Chee Shiu, M. Nalliah and K. Premalatha, “Construction of local antimagic 3-colorable graphs of fixed even size – matrix approach”, arXiv:2404.18049 (2024).

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