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 $\mathcal{H}$, the edge Mostar invariant is describe as $Mo_{e}(\mathcal{H})= \sum\limits_{gx\in E(\mathcal{H})} \left|m_{\mathcal{H}}(g)-m_{\mathcal{H}}(x)\right|$, where $m_{\mathcal{H}}(g)$ (or $m_{\mathcal{H}}(x)$) is the number of edges of $\mathcal{H}$ 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 $\mathfrak{C}(n,s)$, where $s$ is the number of cycles.