Edge Mostar Indices of Cacti Graph With Fixed Cycles - Yasmeen, Farhana; Akhter, Shehnaz; Ali, Kashif; Rizvi, Syed Tahir Raza (Frontiers in Chemistry, 2021)
Topological invariants are the significant invariants which are used to study the physico-chemical and thermodynamic characteristics of chemical compound. Recently a new bond additive invariant named as Mostar invariant is introduced. For any connected graph H, the edge Mostar invariant is describe as Mo_e(H)= _gxE(H) |m_H(g)-m_H(x)|, where m_H(g) (or m_H(x)) is the number of edges of H lying closer to vertex g (or x) than to the vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this paper, we compute the greatest edge Mostar invariant for cacti graph with fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graph in C(n,s), where s is the number of cycles.