Finance

Graph

Topological index

Enhanced Data Rates for GSM Evolution

Order (exchange)

Degree (music)

Simple graph

Mathematics

Biology

Evolutionary biology

Computer science

Acoustics

Weight function

Philosophy

Function (biology)

Economics

Simple (philosophy)

Telecommunications

Vertex (graph theory)

Combinatorics

Connectivity

Statistics

Epistemology

Mathematical analysis

Upper and lower bounds

Discrete mathematics

Physics

match Communications in Mathematical and in Computer Chemistry

For a simple graph G, d u denotes the degree of a vertex u in G. Let f (x, y) be a symmetric real function in two variables, and define the weight w(e) of an edge e = uv of G by w(e) = f (d u , d v ).Then the topological index T I f (G) of G defined by a degree-based edge-weight function f (x, y) is given asy) satisfies some of following properties: f 1 > 0, f 11 > 0, f 12 ≥ 0, f 111 ≥ 0 and for any, we obtain some upper bounds and lower bounds for the topological index T I f (G) and give some graphs of given order and size achieving the bounds.For graphs with small size, we characterize the graphs with maximal and minimal values of the index T I f (G).

Extremal Graphs for Topological Index Defined by a Degree-Based Edge-Weight Function