AbstractLet $$G=(V,E)$$
G
=
(
V
,
E
)
be a graph and $$e=uv\in E$$
e
=
u
v
∈
E
. Define $$n_u(e,G)$$
n
u
(
e
,
G
)
be the number of vertices of G closer to u than to v. The number $$n_v(e,G)$$
n
v
(
e
,
G
)
can be defined in an analogous way. The Mostar index of G is a new graph invariant defined as $$Mo(G)=\sum _{uv\in E(G)}|n_u(uv,G)-n_v(uv,G)|$$
M
o
(
G
)
=
∑
u
v
∈
E
(
G
)
|
n
u
(
u
v
,
G
)
-
n
v
(
u
v
,
G
)
|
. The edge version of Mostar index is defined as $$Mo_e(G)=\sum _{e=uv\in E(G)} |m_u(e|G)-m_v(G|e)|$$
M
o
e
(
G
)
=
∑
e
=
u
v
∈
E
(
G
)
|
m
u
(
e
|
G
)
-
m
v
(
G
|
e
)
|
, where $$m_u(e|G)$$
m
u
(
e
|
G
)
and $$m_v(e|G)$$
m
v
(
e
|
G
)
are the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, respectively. Let G be a connected graph constructed from pairwise disjoint connected graphs $$G_1,\ldots ,G_k$$
G
1
,
…
,
G
k
by selecting a vertex of $$G_1$$
G
1
, a vertex of $$G_2$$
G
2
, and identifying these two vertices. Then continue in this manner inductively. We say that G is a polymer graph, obtained by point-attaching from monomer units $$G_1,\ldots ,G_k$$
G
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.
A new graph invariant arises in toric topology