THE RESISTANCE DISTANCE AND KIRCHHOFF INDEX OF THE k-TH SEMI-TOTAL POINT GRAPHS
نویسندگان
چکیده
The k-th semi-total point graph R(G) of a graph G, is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of the edge considered. In this paper, we obtain formulas for the resistance distance and Kirchhoff index of R(G).
منابع مشابه
On the Kirchhoff Index of Graphs
Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ . . .≥ μn−1 > μn = 0. The Kirchhoff index of G is defined as Kf = Kf(G) = n∑n−1 k=1 1/μk. In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus–Gaddum-type result for the Kirch...
متن کاملMaximizing Kirchhoff index of unicyclic graphs with fixed maximum degree
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.
متن کاملOn hyper-Kirchhoff index
The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...
متن کاملBounds for the Kirchhoff Index of Bipartite Graphs
A m,n -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell D n, a, b consists of the path Pn−a−b together with a independent vertices adjacent to one pendent vertex of Pn−a−b and b independent vertices adjacent to the other pendent vertex of Pn−a−b. In this paper, firstly, we show that, among m,n bipartite gra...
متن کاملFurther Results regarding the Degree Kirchhoff Index of Graphs
Let G be a connected graph with vertex set V.G/. The degree Kirchhoff index of G is defined as S .G/D P fu;vg V.G/ d.u/d.v/R.u;v/, where d.u/ is the degree of vertex u, and R.u;v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result fo...
متن کامل