aspg-39-3077-1792222480 20261017073440 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Neutrosophic and Information Fusion NIF 2836-7863 2024 4 1 Barbara Charchekhandra Jadavpur University, Department Of Mathematics, Kolkata, India The basis number b(G) of a graph G is defined to be the smallest positive integer k such that G has a k-fold basis for its cycle space. We seek an upper bound for b(G1 +G2 +G3 +G4). We prove that if G1, G2, G3, and G4 are connected vertex-disjoint graphs and each has a spanning tree of vertex degree at most 4, then b(G1 +G2 +G3 +G4) ≤ max{4,b(G1) + 1,b(G2) + 2,b(G3) + 2,b(G4) + 1}. The basis number of the quadruple join of paths is also studied. In particular, we prove that b(Pm +Pn +Pp +Pt ) = 4, m,t ≥ 5 and n, p ≥ 6. 2024 01 04 3077 https://creativecommons.org/licenses/by/4.0/ 10.54216/NIF.040101 https://americaspg.com/journal/39/article/3077 https://americaspg.com/storage/articles/manuscripts/01M3N6784QB0PK2PTFJ1AB6SXT.pdf