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Some results on the strongly annihilator ideal graph of a lattice | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 بهمن 1403 اصل مقاله (478.15 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29956.2240 | ||
| نویسندگان | ||
| Vikas Kulal* 1؛ Anil Khairnar2 | ||
| 1Department of Applied science and humanities, School of engineering and sciences, MIT Art, Design and Technology University, Pune-412 201, India | ||
| 2Department of Mathematics, Abasaheb Garware College, Pune-411 004, India | ||
| چکیده | ||
| For a lattice $L$, the strongly annihilator ideal graph of $L$ is denoted by $SAnnIG(L)$. It is a graph with the vertex set, which consists of all ideals in $L$ that have nontrivial annihilators such that any two distinct vertices $I$ and $J$ are adjacent in $SAnnIG(L)$ if and only if the annihilator of $I$ contains a nonzero element of $J$ and the annihilator of $J$ contains a nonzero element of $I$. In this paper, we determine the radius, circumference, and domination number of $SAnnIG(L)$. We obtain necessary and sufficient conditions for $SAnnIG(L)$ to be in the class of paths, cycles, unicyclic, triangle-free, trees, complete multipartite, split or claw-free graphs. Among other results, we study the affinity between the strongly annihilator ideal and the annihilator ideal graph of a lattice. | ||
| کلیدواژه‌ها | ||
| Lattice؛ ideal؛ domination number and strongly annihilator ideal graph | ||
| مراجع | ||
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