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On detour edge cover pebbling number for some classes of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آبان 1405 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30564.2533 | ||
| نویسندگان | ||
| Vincylin S* ؛ I. Gnanaselvi | ||
| Department of Mathematics, Sarah Tucker College, Tirunelveli, Tamilnadu, India. | ||
| چکیده | ||
| Graph pebbling is a technique used to optimize the movement of resources through a network, focusing on efficient transit and allocation. Given a connected graph G, an edge pebbling move involves the removal of two pebbles from one edge and the addition of one pebble to an adjacent edge, while the other pebble will be discarded from the play. In this paper, we carry out the edge pebbling move in the concepts of detour pebbling and cover pebbling to arrive a new graph invariant called the detour edge cover pebbling number. We compute the edge detour distance between two edges with repeated vertices. An edge detour path between eu and ev is a sequence of edges P∗e = {eu, e1, e2,..., ek, ev} such that ei ∩ ei+1= /0, no edge appears more than once in the sequence and repeated vertices are allowed. Thus, the edge detour distance between eu and ev, d∗(eu, ev) = |P∗e|-1 where |P∗e| is the total number of edges in the edge detour path. The detour edge cover pebbling number, f∗ec(G), is the minimum number of pebbles required to cover all the edges of G with at least one pebble each on them after a sequence of pebbling moves by using edge detour paths. The strategy of detour edge cover pebbling number is applied to some standard graphs and staircase graphs (S1, n), n ≥ 4. Also, we give an example that offer grounds for the results and some applications are being discussed. | ||
| کلیدواژهها | ||
| Edge pebbling move؛ Edge detour path؛ Edge detour distance؛ Detour edge cover pebbling number؛ staircase graph | ||
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