By the induced character theory, we first establish the irreducible decomposition of a
permutation representation. Then, using it as a unified tool, we derive a decomposition …

Given a graph G with vertex set V (G)= V and edge set E (G)= E, let Gl be the line graph and
Gc the complement of G. Let G0 be the graph with V (G0)= V and with no edges, G1 the …

The existence of a homomorphism between two digraphs often implies many structural
properties. We collect in this paper some characterizations of various digraph …

Abstract Let π={V 1,…, V r} be an equitable partition of the vertex set of a directed graph
(digraph) X. It is well known that the characteristic polynomial ϕ (X/π, x) of a quotient graph …

For an abelian group Γ, a formula to compute the characteristic polynomial of a Γ-graph has
been obtained by Lee and Kim [Characteristic polynomials of graphs having a semi-free …

Let D be a digraph with vertex set V and arc set. In the paper [Deng A, Kelmans A. Spectra of
digraph transformations. Linear Algebra Appl. 2013; 439: 106–132], the xyz-transformation …

We give a decomposition formula for the characteristic polynomials of ramified uniform
covers of digraphs. Similarly, we obtain a decomposition formula for the characteristic …

Let A (λ, D) be the adjacency characteristic polynomial of a digraph D. In the paper Deng
and Kelmans (2013) the so-called (xyz)-transformation D xyz of a simple digraph D was …

We extend a balanced signed graph to a digraph, and present a necessary and sufficient
condition for a signed digraph to be balanced. Moreover, we give another necessary and …

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