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On the Metric Dimension and Spectrum of Graphs | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 شهریور 1403 اصل مقاله (471.94 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2024.29109.1850 | ||
نویسندگان | ||
Mohammad Farhan1؛ Edy Tri Baskoro* 2، 3 | ||
1Master Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia | ||
2Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia | ||
3Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia | ||
چکیده | ||
The algebraic approach to graph theoretical problems has been extensively studied by looking at the spectrum of a graph's representation matrix. In this paper, we investigate some relationships between the metric dimension of a graph $G$ and its nullity, that is, the multiplicity of eigenvalue $0$ in the adjacency matrix of $G$, and the eigenvalues of its Laplacian and distance matrices. Furthermore, we also present a relationship between the metric dimension of a graph and its nullity, using twin classes. | ||
کلیدواژهها | ||
metric dimension؛ spectrum؛ nullity؛ twin classes | ||
مراجع | ||
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