English

Mostar index and edge Mostar index of polymers

Combinatorics 2021-06-15 v1

Abstract

Let G=(V,E)G=(V,E) be a graph and e=uvEe=uv\in E. Define nu(e,G)n_u(e,G) be the number of vertices of GG closer to uu than to vv. The number nv(e,G)n_v(e,G) can be defined in an analogous way. The Mostar index of GG is a new graph invariant defined as Mo(G)=uvE(G)nu(uv,G)nv(uv,G)Mo(G)=\sum_{uv\in E(G)}|n_u(uv,G)-n_v(uv,G)|. The edge version of Mostar index is defined as Moe(G)=e=uvE(G)mu(eG)mv(Ge)Mo_e(G)=\sum_{e=uv\in E(G)} |m_u(e|G)-m_v(G|e)|, where mu(eG)m_u(e|G) and mv(eG)m_v(e|G) are the number of edges of GG lying closer to vertex uu than to vertex vv and the number of edges of GG lying closer to vertex vv than to vertex uu, respectively. Let GG be a connected graph constructed from pairwise disjoint connected graphs G1,,GkG_1,\ldots ,G_k by selecting a vertex of G1G_1, a vertex of G2G_2, and identifying these two vertices. Then continue in this manner inductively. We say that GG is a polymer graph, obtained by point-attaching from monomer units G1,...,GkG_1,...,G_k. In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their Mostar and edge Mostar indices.

Keywords

Cite

@article{arxiv.2106.06562,
  title  = {Mostar index and edge Mostar index of polymers},
  author = {Nima Ghanbari and Saeid Alikhani},
  journal= {arXiv preprint arXiv:2106.06562},
  year   = {2021}
}

Comments

23 pages, 18 Figures