| Title: | On the metric subgraphs of a graph |
|---|
| Authors: | ID Hu, Yanan (Author)
ID Zhan, Xingzhi (Author) |
|---|
| Files: |  AMC_Hu_Yanan_Zhan_Xingzhi_2025.pdf (533,77 KB)
MD5: 4B5F4704029CE1F0DD7FAE1F1BECA81F
 https://amc-journal.eu/index.php/amc/article/view/2992
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
|
|---|
| Abstract: | The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order n whose metric subgraphs are all paths if and only if n ≥ 13 and the smallest size of such a graph of order 13 is 22; (2) there exists a graph of order n whose metric subgraphs are all cycles if and only if n ≥ 15, and there are exactly three such graphs of order 15; (3) for every integer k ≥ 3, we determine the possible orders for the existence of a graph whose metric subgraphs are all connected k-regular graphs; (4) there exists a graph of order n whose metric subgraphs are connected and pairwise isomorphic if and only if n ≥ 24 and n is divisible by 3. An unsolved problem is posed. |
|---|
| Keywords: | center, annulus, periphery, metric subgraphs, path, cycle |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 11.02.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 13 |
|---|
| Numbering: | Vol. 25, no. 1, [article no.] P1.03 |
|---|
| PID: | 20.500.12556/RUP-21747  |
|---|
| ISSN: | 1855-3966 |
|---|
| UDC: | 519.17 |
|---|
| eISSN: | 1855-3974 |
|---|
| DOI: | 10.26493/1855-3974.2992.a6d |
|---|
| Publication date in RUP: | 16.09.2025 |
|---|
| Views: | 393 |
|---|
| Downloads: | 15 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
