آمار
| تعداد نشریات | 6 |
| تعداد شماره‌ها | 129 |
| تعداد مقالات | 1,616 |
| تعداد مشاهده مقاله | 1,853,238 |
| تعداد دریافت فایل اصل مقاله | 1,715,884 |
On the Identification Numbers of Lobster Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 تیر 1404 اصل مقاله (649.4 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29836.2183 | ||
| نویسندگان | ||
| Mark Anthony C. Tolentino* ؛ Luis Jr. S. Silvestre؛ Richwell T. Chan Sim؛ Amir Jann Erikson E. Diga؛ Althea Julia R. Loyola | ||
| Department of Mathematics, Ateneo de Manila University, Quezon City, Philippines | ||
| چکیده | ||
| Given a nontrivial connected undirected graph $G$ with diameter $d$, a vertex coloring $c$ of $G$ that uses only the colors red and white induces, for each $v \in V(G)$, the $d$-vector $\vec{d}(v) = [a_1 a_2 \cdots a_d]$, where each $a_i$ is equal to the number of red vertices of distance $i$ from $v$. Then $c$ is called an ID-coloring of $G$ if $\vec{d}(v) \neq \vec{d}(w)$ for all distinct $v,w \in V(G)$. If $G$ has at least one ID-coloring, then it is called an ID-graph and its identification number $ID(G)$ is defined to be the minimum number of red vertices among all ID-colorings of $G$. The notions of ID-colorings and identification number have been shown to be equivalent to the notions of multiset resolving sets and multiset dimension, respectively. Previous works on this topic have focused on characterizing ID-caterpillars and ID-lobsters and on the identification numbers of some ID-caterpillars. In this paper, we focus on the identification numbers of ID-lobsters. Specifically, we establish a sharp lower bound for the identification number of all ID-lobsters. Furthermore, we characterize and determine the identification numbers of all uniform ID-lobsters. | ||
| کلیدواژه‌ها | ||
| identification colorings؛ multiset dimension؛ lobster graph | ||
| مراجع | ||
|
[1] R.T. Chan Sim, A.J.E.E. Diga, and A. J.R. Loyola, Identification coloring of lobster graphs, Undergraduate thesis, Ateneo de Manila University, 2024.
[2] G. Chartrand, Y. Kono, and P. Zhang, Distance vertex identification in graphs, J. Interconnect. Netw. 21 (2021), no. 01, Article ID: 2150005. https://doi.org/10.1142/S0219265921500055
[3] Y. Hafidh, R. Kurniawan, S. Saputro, R. Simanjuntak, S. Tanujaya, and S. Uttunggadewa, Multiset dimensions of trees, 2019, https://doi.org/10.48550/arXiv.1908.05879
[4] A. Hakanen and I.G. Yero, Complexity and equivalency of multiset dimension and ID-colorings, 2023, https://doi.org/10.48550/arXiv.2303.06986
[5] S. Isariyapalakul, V. Khemmani, and W. Pho-on, The multibases of symmetric caterpillars, J. Math. 2020 (2020), no. 1, Article ID: 5210628. https://doi.org/10.1155/2020/5210628
[6] V. Khemmani and S. Isariyapalakul, The characterization of caterpillars with multidimension 3, Thai J. Math. Annual Meeting in Mathematics 2019 (2020), 247–259.
[7] Y. Kono and P. Zhang, Vertex identification in trees, Discrete Math. Lett. 7 (2021), 66–73. https://doi.org/10.47443/dml.2021.0042
[8] Y. Kono and P. Zhang, A note on the identification numbers of caterpillars, Discrete Math. Lett. 8 (2022), 10–15. https://doi.org/10.47443/dml.2021.0073
[9] Y. Kono and P. Zhang, Vertex identification in grids and prisms, J. Interconnect. Netw. 22 (2022), no. 02, Article ID: 2150019. https://doi.org/10.1142/S0219265921500195
[10] R.M. Marcelo, M.A.C. Tolentino, A.D. Garciano, M.J.P. Ruiz, and J.C. Buot, On the vertex identification spectra of grids, J. Interconnect. Netw. 25 (2025), no. 1, Article ID: 2450002. https://doi.org/10.1142/S0219265924500026
[11] V. Saenpholphat, On multiset dimension in graphs, Academic SWU 1 (2009), 193–202.
[12] R. Simanjuntak, P. Siagian, and T. Vetrik, The multiset dimension of graphs, 2019, https://doi.org/10.48550/arXiv.1711.00225 | ||
|
آمار تعداد مشاهده مقاله: 238 تعداد دریافت فایل اصل مقاله: 237 |
||