Shaghayegh Rahmani - Academia.edu (original) (raw)
Papers by Shaghayegh Rahmani
Iranian journal of mathematical chemistry, 2019
For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to ... more For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes.
Symmetry
Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with... more Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240.
arXiv: Combinatorics, 2019
The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalizat... more The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph GGG of order at least 2 and SsubseteqV(G)S\subseteq V(G)SsubseteqV(G), the Steiner distance dG(S)d_G(S)dG(S) of the set SSS of vertices in GGG is the minimum size of a connected subgraph whose vertex set contains or connects SSS. In this paper, we introduce the concept of the Steiner (revised) Szeged index ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) of a graph GGG, which is a natural generalization of the well-known (revised) Szeged index of chemical use. We determine the Szk(G)Sz_k(G)Szk(G) for trees in general. Then we give a formula for computing the Steiner Szeged index of a graph in terms of orbits of automorphism group action on the edge set of the graph. Finally, we give sharp upper and lower bounds of ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) of a connected graph GGG, and establish some of its properties. Formulas of ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) for small and large kkk are also given in this paper.
Iranian Journal of Mathematical Chemistry, 2019
The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalizat... more The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d G (S) of the set S of vertices in G is the minimum size of a connected subgraph whose vertex set contains or connects S. In this paper, we introduce the concept of the Steiner (revised) Szeged index (rSz k (G)) Sz k (G) of a graph G, which is a natural generalization of the well-known (revised) Szeged index of chemical use. We determine the Sz k (G) for trees in general. Then we give a formula for computing the Steiner Szeged index of a graph in terms of orbits of automorphism group action on the edge set of the graph. Finally, we give sharp upper and lower bounds of (rSz k (G)) Sz k (G) of a connected graph G, and establish some of its properties. Formulas of (rSz k (G)) Sz k (G) for small and large k are also given in this paper.
Iranian journal of mathematical chemistry, 2019
For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to ... more For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes.
Symmetry
Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with... more Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240.
arXiv: Combinatorics, 2019
The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalizat... more The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph GGG of order at least 2 and SsubseteqV(G)S\subseteq V(G)SsubseteqV(G), the Steiner distance dG(S)d_G(S)dG(S) of the set SSS of vertices in GGG is the minimum size of a connected subgraph whose vertex set contains or connects SSS. In this paper, we introduce the concept of the Steiner (revised) Szeged index ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) of a graph GGG, which is a natural generalization of the well-known (revised) Szeged index of chemical use. We determine the Szk(G)Sz_k(G)Szk(G) for trees in general. Then we give a formula for computing the Steiner Szeged index of a graph in terms of orbits of automorphism group action on the edge set of the graph. Finally, we give sharp upper and lower bounds of ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) of a connected graph GGG, and establish some of its properties. Formulas of ($rSz_k(G)$) Szk(G)Sz_k(G)Szk(G) for small and large kkk are also given in this paper.
Iranian Journal of Mathematical Chemistry, 2019
The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalizat... more The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d G (S) of the set S of vertices in G is the minimum size of a connected subgraph whose vertex set contains or connects S. In this paper, we introduce the concept of the Steiner (revised) Szeged index (rSz k (G)) Sz k (G) of a graph G, which is a natural generalization of the well-known (revised) Szeged index of chemical use. We determine the Sz k (G) for trees in general. Then we give a formula for computing the Steiner Szeged index of a graph in terms of orbits of automorphism group action on the edge set of the graph. Finally, we give sharp upper and lower bounds of (rSz k (G)) Sz k (G) of a connected graph G, and establish some of its properties. Formulas of (rSz k (G)) Sz k (G) for small and large k are also given in this paper.