A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path
Priscilla Paul, S. Syed Ali Fathima · Indian Journal of Science and Technology · 2023
Objectives: To find the edge pebbling number and covering cover edge pebbling number of friendship graphs. Methods: The possible minimum edge covering set of the friendship graph is considered and the set with the minimum pebble requirement covering all vertices is selected. Findings: Obtained the modified result of edge pebbling number of friendship graph, defined the covering cover edge pebbling number of a graph G, and covering cover edge pebbling number for friendship graphs, odd path and even path is found. Also found that friendship graphs are edge demonic. Novelty: Finding the covering cover edge pebbling number of a graph plays a vital role in optimization problems. Since all the vertices are covered, for instance the locations of mobile towers can be considered as edges and residential areas as vertices, and network signals can be modified according to the number of pebbles. Keywords: Friendship Graphs; Odd Path; Even Path; Minimum Edge Covering Set; Edge Pebbling Number; Edge Demonic; Covering Cover Edge Pebbling Number