### Discrete Mathematics

We study various graph invariants in several classes of graphs. Typically the objective is to characterise extremal graphs and estimate extremal values of the invariants. Most of the invariants that we worked on so far are counting based invariants with application in Chemistry, such as Merrifield-Simmons index, Hosoya index, Estrada index, energy of graphs. I some occasions, we also have worked with number of infima closed sets in a rooted tree, number of walks, number of subtrees, spectral moments and spectral radius. So we mainly use combinatorial and algebraic tools.

Below is a list of our most recent results:

- Maximum Wiener index of trees with given segment sequence, accepted for publication in MATCH Communications in Mathematical and in Computer Chemistry; with S. Wagner and H. Wang. Preprint.
- Graphs with maximal Hosoya index and minimal Merrifield-Simmons index, Discrete Mathematics, 329 (2014) 77-87. With Z. Zhu, C. Yuan and S. Wagner. Full text.
- Spectral moment of trees with given degree sequence, Linear Algebra Appl. 439 (2013) 3980-4002. With S. Wagner. Preprint.
- Greedy trees, subtrees and antichains, Electron. J. Combin. 20(3) (2013), 28. With S. Wagner and H. Wang, Free full text.
- Energy, Hosoya index and Merrifield-Simmons index of trees with prescribed degree sequence, Discrete Appl. Math. 161 (2013) 724-741. Full text.
- More Trees with Large Energy and Small Size, MATCH Commun. Math. Comput. Chem., 68 (2012) 697-702; with I. Gutman, B. Furtula and M. Cvetic. Free full text.
- More Trees with Large Energy, MATCH Commun. Math. Comput. Chem., 68 (2012) 675-695. Free full text.
- Unicyclic graphs with large energy, Linear Algebra and its Applications, 435 (2011) 1399-1414; with S. Wagner. Full text.

We would welcome MSc or PhD candidates, or postdoc excited to work on an Extremal Graph theory project. For more details, contact Eric Andriantiana.

Last Modified**: Thu, 08 Sep 2016 16:31:56 SAST**