| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4654109 | European Journal of Combinatorics | 2010 | 5 Pages |
Abstract
It is shown that the graphs for which the Szeged index equals ‖G‖⋅∣G∣24 are precisely connected, bipartite, distance-balanced graphs. This enables us to disprove a conjecture proposed in [M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, S.G. Wagner, Some new results on distance-based graph invariants, European J. Combin. 30 (2009) 1149–1163]. Infinite families of counterexamples are based on the Handa graph, the Folkman graph, and the Cartesian product of graph. Infinite families of distance-balanced, non-regular graphs that are prime with respect to the Cartesian product are also constructed.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Aleksandar Ilić, Sandi Klavžar, Marjan Milanović,