{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T03:52:58Z","timestamp":1768881178503,"version":"3.49.0"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"Science Found of Qinghai Province","award":["2021-ZJ-703"],"award-info":[{"award-number":["2021-ZJ-703"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> Lattice cryptosystem is a kind of public key cryptosystem which is resistant to quantum computing attacks. Cryptanalysis is involved in the study of lattice cryptanalysis. There are many problems such as the interdisciplinary characteristics are obvious and the research methods tend to be diversified. This paper defines new graph total colorings: graceful-difference total coloring, odd-edge graceful difference total coloring. It is proven that (1) if a connected bipartite graph [Formula: see text] recognizes ordered graceful-difference labeling, the bipartite graph [Formula: see text] obtained by adding [Formula: see text] leaves to connected bipartite graph [Formula: see text] recognizes a graceful-difference total coloring, (2) in order to establish a random coloring graphic lattice, two operations are given to design the graphic lattice. The proof of the theorem can be transformed into a feasible and effective algorithm. <\/jats:p>","DOI":"10.1142\/s1793830923501197","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T14:17:28Z","timestamp":1703686648000},"source":"Crossref","is-referenced-by-count":1,"title":["Graphic lattice constructed by graceful-difference total colorings"],"prefix":"10.1142","volume":"16","author":[{"given":"Xiaohui","family":"Zhang","sequence":"first","affiliation":[{"name":"Computer College of Qinghai Normal University, Xining 810001, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shumin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, P. R. China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengfu","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, P. R. China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. 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