Detour Monophonic Vertex Cover Pebbling Number (DMVCPN) of Some Standard Graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929371088945152 |
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| author | Rani, K. Christy Dhivviyanandam, I. |
| author_facet | Rani, K. Christy Dhivviyanandam, I. |
| contents | Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Pebbling shift is a deletion of two pebbles from a vertex and a placement of one pebble at a neighbouring vertex. The vertex cover set, $D_{vc}$ for graph $G$ is the subset of $V(G)$ such that every edge in $G$ has at least one end in $D_{vc}$. A detour monophonic path is considered to be a longest chordless path between two non adjacent vertices $x$ and $y$. A detour monophonic vertex cover pebbling number, $μ_{vc}(G),$ is a minimum number of pebbles required to cover all the vertices of the vertex cover set of $G$ with at least one pebble each on them after the transformation of pebbles by using detour monophonic paths. We determine the detour monophonic vertex cover pebbling number (DMVCPN) of the cycle, path, fan, and wheel graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detour Monophonic Vertex Cover Pebbling Number (DMVCPN) of Some Standard Graphs Rani, K. Christy Dhivviyanandam, I. Combinatorics Optimization and Control 05C12, 05C25, 05C38, 05C76, and 05C99 G.2.1 Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Pebbling shift is a deletion of two pebbles from a vertex and a placement of one pebble at a neighbouring vertex. The vertex cover set, $D_{vc}$ for graph $G$ is the subset of $V(G)$ such that every edge in $G$ has at least one end in $D_{vc}$. A detour monophonic path is considered to be a longest chordless path between two non adjacent vertices $x$ and $y$. A detour monophonic vertex cover pebbling number, $μ_{vc}(G),$ is a minimum number of pebbles required to cover all the vertices of the vertex cover set of $G$ with at least one pebble each on them after the transformation of pebbles by using detour monophonic paths. We determine the detour monophonic vertex cover pebbling number (DMVCPN) of the cycle, path, fan, and wheel graphs. |
| title | Detour Monophonic Vertex Cover Pebbling Number (DMVCPN) of Some Standard Graphs |
| topic | Combinatorics Optimization and Control 05C12, 05C25, 05C38, 05C76, and 05C99 G.2.1 |
| url | https://arxiv.org/abs/2406.01009 |