Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</...Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.展开更多
Let G be a permutation group positive integer. Then the movement of G on a set Ω with no fixed points in Ω, and m be a is defined as move（G）：=supГ{[Г^9 ／Г｜｜g ∈ G}. It F was shown by Praeger that if move（...Let G be a permutation group positive integer. Then the movement of G on a set Ω with no fixed points in Ω, and m be a is defined as move（G）：=supГ{[Г^9 ／Г｜｜g ∈ G}. It F was shown by Praeger that if move（G） = m, then ｜Ω｜ ≤ 3m ＋ t - 1, where t is the number of G-orbits on ≤. In this paper, all intransitive permutation groups with degree 3m ＋ t - 1 which have maximum bound are classified. Indeed, a positive answer to her question that whether the upper bound ｜Ω｜ = 3m ＋ t - 1 for ｜Ω｜ is sharp for every t 〉 1 is given.展开更多
文摘Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.
文摘Let G be a permutation group positive integer. Then the movement of G on a set Ω with no fixed points in Ω, and m be a is defined as move（G）：=supГ{[Г^9 ／Г｜｜g ∈ G}. It F was shown by Praeger that if move（G） = m, then ｜Ω｜ ≤ 3m ＋ t - 1, where t is the number of G-orbits on ≤. In this paper, all intransitive permutation groups with degree 3m ＋ t - 1 which have maximum bound are classified. Indeed, a positive answer to her question that whether the upper bound ｜Ω｜ = 3m ＋ t - 1 for ｜Ω｜ is sharp for every t 〉 1 is given.
