Per-spectral characterizations of graphs with extremal per-nullity

Characterizations of Strength Extremal Graphs

With graphs considered as natural models for many network design problems, edge connectivity κ ′(G) and maximum number of edge-disjoint spanning trees τ(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G (see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–25...

Per-spectral and adjacency spectral characterizations of a complete graph removing six edges

Cámara and Haemers (2014) investigatedwhen a complete graphwith some edges deleted is determined by its adjacency spectrum (DAS for short). They claimed: for anym ≥ 6 and every large enough n one can obtain graphswhich are not DAS by removingm edges from a complete graph Kn. LetGn denote the set of all graphs obtained from a complete graph Kn by deleting six edges. In this paper, we show that a...

Graphs Drawn with Few Crossings Per Edge

Given a simple graph G, let v(G) and e(G) denote its number of vertices and edges, respectively. We say that G is drawn in the plane if its vertices are represented by distinct points of the plane and its edges are represented by Jordan arcs connecting the corresponding point pairs but not passing through any other vertex. Throughout this paper, we only consider drawings with the property that ...

Regular graphs with maximal energy per vertex

Spectral characterizations of sandglass graphs

The sandglass graph is obtained by appending a triangle to each pendant vertex of a path. It is proved that sandglass graphs are determined by their adjacency spectra as well as their Laplacian spectra. © 2009 Elsevier Ltd. All rights reserved.