Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
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Title: Spectral Properties of the eccentricity matrix for special classes of graphs
Speaker: | Lavanya Selvaganesh |
Affiliation: | Indian Institute of Technology (BHU) Varanasi |
Zoom | Contact Soffia Arnadottir |
Abstract:
Eccentricity matrix, another graph matrix, was originally proposed, as $D_{MAX}$ matrix, by Randi\'c in 2013 and redefined by Wang et al. in 2018 by using the concept of the eccentricities of vertices. In this talk, we will discuss the irreducibility and the spectral properties of the eccentricity matrix for special classes of graphs, such as trees, coalescence of complete graphs (windmill graphs), coalescence of cycles (Dutch windmill graphs).
In 2018, Wang et al. posed a conjecture which states that ``Among the trees on $n$ vertices, the tree with a vertex of degree $n-2$ has the minimum Ecc-spectral radius". We will also discuss the status of this conjecture.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.