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Join standard graph of a lattice | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 مهر 1404 اصل مقاله (603.43 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30680.2577 | ||
| نویسندگان | ||
| N Aishwarya Nayak1؛ Pallavi P2؛ Syam Prasad Kuncham1؛ Tapatee S2؛ Harikrishnan P K* 1 | ||
| 1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India | ||
| 2Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India | ||
| چکیده | ||
| In this paper, we introduce and investigate the join standard graph $G_S(L)$ of a finite lattice $L$. We explore structural properties of the graph such as connectedness, girth, and provide necessary and sufficient conditions for the existence of universal and isolated vertices. We show that a lattice homomorphism $\varphi$ from $L_1$ to $L_2$ induces a graph homomorphism between $G_S(L_1)$ and $G_S(L_2)$. We further analyze the relationship between the graph of a lattice product and the product of graphs of its constituent lattices. Subsequently, we establish a condition under which the graph becomes hypertriangulated. We prove that the graph $G_S(L)$ is complemented if and only if the underlying lattice has cardinality at most two. Finally, we provide a criterion under which the subgraph $G_S(L)-1$ becomes disconnected. | ||
| کلیدواژهها | ||
| standard element؛ lattice؛ cartesian product؛ totally disconnected | ||
| مراجع | ||
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