The extremal values of some topological indices in bipartite graphs with a given matching number

On extremal bipartite graphs with a given connectivity

“…But from another perspective, many important topological indices have the monotonicity [4], i.e., decrease (or increase, respectively) with addition of edges, such as the Wiener index, the eccentricity distance sum, the Kirchhoff index, the Merrifield-Simmons index are monotonically decreasing with the addition of edges, and the Zagreb index, the Hosoya index, the atom-bond connectivity index, the Estrada index, the matching energy are monotonically increasing with the addition of edges.…”

“…After that, these results for bipartite graphs haven been extended to the distance Laplacian spectral radius by Liu et al [23], to the Wiener index by Li and Song [18] and the Estrada index by Huang et al [16]. On the basis of the monotonicity, unified approaches for various topological indices of graphs (or bipartite graphs) in terms of some kinds of graph parameters were proposed in [4,5,29].…”

The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

“…Let G + uv be the graph obtained from G by adding an edge uv ∈ E(G). Let I(G) be a graph invariant, if I(G + uv) > I(G) (or I(G + uv) < I(G), respectively) for any edge uv ∈ E(G), then we call I(G) a monotonic increasing (or decreasing, respectively) graph invariant with the addition of edges [5]. Let G n,m,k be the set of graphs with order n and vertex k-…”

“…In [5][6][7], the authors have researched several monotonic topological indices in G n,m,2 , such as the Kirchhoff index, the spectral radius, the signless Laplacian spectral radius, the modified-Wiener index, the connective eccentricity index, and so on. Inspired by these results, we extend the parameter of graph partition from two-partiteness to arbitrary k-partiteness.…”

Further results on computation of topological indices of certain networks

“…A topological index is a numerical parameter mathematically derived from the graph structure. The topological indices have been found to be useful for establishing correlations between the structure of a molecular compound and its physicochemical properties or biological activity [1–8].…”