Some new results on distance-based graph invariants
European Journal of Combinatorics
Finding the longest isometric cycle in a graph
Discrete Applied Mathematics
Note: A characterization of block graphs
Discrete Applied Mathematics
European Journal of Combinatorics
On a conjecture about the Szeged index
European Journal of Combinatorics
Use of the Szeged index and the revised Szeged index for measuring network bipartivity
Discrete Applied Mathematics
Discrete Applied Mathematics
Handbook of Product Graphs, Second Edition
Handbook of Product Graphs, Second Edition
Mathematical and Computer Modelling: An International Journal
Bicyclic graphs with extremal values of PI index
Discrete Applied Mathematics
Note: Wiener index versus Szeged index in networks
Discrete Applied Mathematics
Bicyclic graphs with maximal revised Szeged index
Discrete Applied Mathematics
The (revised) Szeged index and the Wiener index of a nonbipartite graph
European Journal of Combinatorics
Wiener index in weighted graphs via unification of Θ*-classes
European Journal of Combinatorics
| Hi-index | 0.00 |
Let W(G) and Sz(G) be the Wiener index and the Szeged index of a connected graph G, respectively. It is proved that if G is a connected bipartite graph of order n=4, size m=n, and if @? is the length of a longest isometric cycle of G, then Sz(G)-W(G)=n(m-n+@?-2)+(@?/2)^3-@?^2+2@?. It is also proved if G is a connected graph of order n=5 and girth g=5, then Sz(G)-W(G)=PI"v(G)-n(n-1)+(n-g)(g-3)+P(g), where PI"v(G) is the vertex PI index of G and P is a cubic polynomial. These theorems extend related results from Chen et al. (2014). Several lower bounds on the difference Sz(G)-W(G) for general graphs G are also given without any condition on the girth.