Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological in...Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.展开更多
Let G be simple connected graph with the vertex and edge sets V (G) and E (G), respectively. The Schultz and Modified Schultz indices of a connected graph G are defined as and , where d (u, v) is the distance between ...Let G be simple connected graph with the vertex and edge sets V (G) and E (G), respectively. The Schultz and Modified Schultz indices of a connected graph G are defined as and , where d (u, v) is the distance between vertices u and v?;dv is the degree of vertex v of G. In this paper, computation of the Schultz and Modified Schultz indices of the Jahangir graphs J5,m is proposed.展开更多
In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has ...In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has to move to the attacked vertex and all the remaining guards are allowed to move to an adjacent vertex or stay in their current position after each attack. If the new formed set of guards is still a dominating set of the graph then we successfully defended the attack. Our goal is to find the minimum number of guards required to eternally protect the graph. We call this number the m-eternal domination number and we denote it by . In this paper we find the eternal domination number of Jahangir graph Js,m for s=2,3 and arbitrary m. We also find the domination number for J3,m .展开更多
文摘Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.
文摘Let G be simple connected graph with the vertex and edge sets V (G) and E (G), respectively. The Schultz and Modified Schultz indices of a connected graph G are defined as and , where d (u, v) is the distance between vertices u and v?;dv is the degree of vertex v of G. In this paper, computation of the Schultz and Modified Schultz indices of the Jahangir graphs J5,m is proposed.
文摘In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has to move to the attacked vertex and all the remaining guards are allowed to move to an adjacent vertex or stay in their current position after each attack. If the new formed set of guards is still a dominating set of the graph then we successfully defended the attack. Our goal is to find the minimum number of guards required to eternally protect the graph. We call this number the m-eternal domination number and we denote it by . In this paper we find the eternal domination number of Jahangir graph Js,m for s=2,3 and arbitrary m. We also find the domination number for J3,m .
