For any real number α, the sum of the α-th powers of the degrees of a (molecular) graph G,
denoted by 0Rα (G), is known as the general zeroth–order Randic index as well as the …

The resistance distance between any two vertices of a graph G is defined as the effective
resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index …

In this work, we propose a novel robustness measure for networks, which we refer to as
Effective Resistance Centrality of a vertex (or an edge), defined as the relative drop of the …

Let G be a simple connected graph with n vertices, m edges, a sequence of vertex degrees
d1≥ d2≥···≥ dn> 0, and D= diag (d1, d2,..., dn) the diagonal matrix of its vertex degrees. If …

In this paper, among all the bipartite graphs with diameter 2 and 3, we characterize the
graphs which have the largest and the smallest Kirchhoff index. Moreover, we characterize …

Let G be a simple graph of order n≥ 2 with m edges. Denote by d1≥ d2≥···≥ dn> 0 the
sequence of vertex degrees and by µ1≥ µ2≥···≥ µn− 1> µn= 0 the Laplacian eigenvalues …

Using electrical networks and majorization we obtain a lower bound for the augmented
Zagreb index in terms of the number of vertices and edges, and the maximum vertex degree …

The Kirchhoff index of a connected graph is the sum of resistance distances between all
unordered pairs of vertices in the graph. In this paper, we determine the minimum Kirchhoff …

The degree Kirchhoff index (or multiplicative degree Kirchhoff index) of a connected simple
graph G is defined as S′(G)=∑{u, v}⊆ V (G) d G (u) d G (v) RG (u, v), where d G (u) is the …

Comparing Laplacian Energy and Kirchhoff Index Page 1 Comparing Laplacian Energy and
Kirchhoff Index Kinkar Ch. Das1,∗, Ivan Gutman2 1Department of Mathematics …