Detour Monophonic Vertex Cover Pebbling Number (DMVCPN) of Some Standard Graphs
K. Christy Rani, I. Dhivviyanandam

TL;DR
This paper introduces the detour monophonic vertex cover pebbling number (DMVCPN), a new graph invariant, and computes it for standard graphs like cycles, paths, fans, and wheels, expanding pebbling theory.
Contribution
It defines DMVCPN, a novel concept in graph pebbling, and provides exact values for several fundamental graph classes, advancing understanding of pebbling dynamics.
Findings
DMVCPN computed for cycle, path, fan, and wheel graphs.
Establishes relationships between DMVCPN and graph structure.
Provides formulas and bounds for DMVCPN in standard graphs.
Abstract
Let be a connected graph with vertex set and edge set . 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, for graph is the subset of such that every edge in has at least one end in . A detour monophonic path is considered to be a longest chordless path between two non adjacent vertices and . A detour monophonic vertex cover pebbling number, is a minimum number of pebbles required to cover all the vertices of the vertex cover set of 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCellular Automata and Applications
