AUTHOR=Yasmeen Farhana , Akhter Shehnaz , Ali Kashif , Rizvi Syed Tahir Raza 

TITLE=Edge Mostar Indices of Cacti Graph With Fixed Cycles

JOURNAL=Frontiers in Chemistry

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2021.693885

DOI=10.3389/fchem.2021.693885

ISSN=2296-2646

ABSTRACT=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.