Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi
graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very …

This is the first full-length book on the major theme of symmetry in graphs. Forming part of
algebraic graph theory, this fast-growing field is concerned with the study of highly …

A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two
orbits of equal size. In this paper, some basic properties and the automorphisms of bi-Cayley …

A graph X is said to be distance-balanced if for any edge uv of X, the number of vertices
closer to u than to v is equal to the number of vertices closer to v than to u. A graph X is said …

The well-known Petersen graph G (5, 2) admits a semi-regular automorphism α acting on
the vertex set with two orbits of equal size. This makes it a bicirculant. It is shown that …

In a graph G a vertex v dominates all its neighbors and itself. A set D of vertices of G is
(vertex) dominating set if each vertex of G is dominated by at least one vertex in D. The …

We consider a family of I-graphs I (n, k, l), which is a generalization of the class of
generalized Petersen graphs. In the present paper, we provide a new method for counting …

The Spectrum of Generalized Petersen Graphs Page 1 The Spectrum of Generalized
Petersen Graphs Ralucca Gera and Pantelimon Stanica ∗ Department of Applied …

The super-connectivity (super-edge-connectivity) of a connected graph G is the minimum
number of vertices (edges) that need to be deleted from G in order to disconnect G without …

It is known that the problem of computing the edge dimension of a graph is NP-hard, and
that the edge dimension of any generalized Petersen graph P (n, k) is at least 3. We prove …