Hamidoune’s connectivity results [11] for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then it is optimally vertex connected. The results are obtained by extending the methods used in [11]. They are used to show that cycle-prefix g...

Eigenvectors of the Laplacian of a cycle graph exhibit the sinusoidal characteristics of the standard DFT basis, and signals defined on such graphs are amenable to linear shift invariant (LSI) operations. In this paper we propose to reduce a generic graph to its vertex-disjoint cycle cover, i.e., a set of subgraphs that are cycles, that together contain all vertices of the graph, and no two sub...

In a properly vertex-colored graphG, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P . If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring ofG. The minimum numbe...

The terminology and notation used but undefined in this paper can be found in [1]. Let G be a graph and we use V (G), E(G), F (G), ∆(G) and δ(G) to denote the vertex set, edge set, face set, maximum degree, and minimum degree of G, respectively. Let dG(x) or simply d(x), denote the degree of a vertex (resp. face) x in G. A vertex (resp. face) x is called a k-vertex (resp. k-face), k-vertex (res...

A tournament T is an orientation of a complete graph, and a feedback vertex set of T is a subset of vertices intersecting every directed cycle of T . We prove that every tournament on n vertices has at most 1.6740 minimal feedback vertex sets and some tournaments have 1.5448 minimal feedback vertex sets. This improves a result by Moon (1971) who showed upper and lower bounds of 1.7170 and 1.475...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...