The complementary prism Γ Γ¯ is constructed from the disjoint union of a graph Γ and its
complement Γ¯ if an edge is added between each pair of identical vertices in Γ and Γ¯. It …

Let F m× n be the set of m× n matrices over a field F. Consider a graph G=(F m× n,∼) with F
m× n as the vertex set such that two vertices A, B∈ F m× n are adjacent if rank (A− B)= 1. We …

A graph G is a pseudo-core if every endomorphism of G is either an automorphism or a
colouring. Let F q be the finite field with q elements and let Alt (m, q)(m≥ 4) be the …

A graph is called a pseudo-core if every endomorphism is either an automorphism or a
colouring. In this paper, we show that every Grassmann graph $ J_q (n, m) $ is a pseudo …

Let SGL n (F 2) be the set of all invertible n× n symmetric matrices over the binary field F 2.
Let Γ n be the graph with the vertex set SGL n (F 2) where a pair of matrices {A, B} form an …

Let r and s be positive integers such that r⩾ 2. Let U and V be vector spaces over fields F
and K, respectively, such that dim⁡ U⩾ 3 and F has at least r+ 1 elements. In this paper, we …

Given a finite simple graph $\Gamma $ on $ n $ vertices its complementary prism is the
graph $\Gamma\bar {\Gamma} $ that is obtained from $\Gamma $ and its complement $\bar …

In this note we consider two related infinite families of graphs, which generalize the Petersen
and the Coxeter graph. The main result proves that these graphs are cores. It is determined …

A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or
a colouring. An interesting problem in graph theory is to distinguish whether a graph is a …

A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or
a colouring. A graph G is a core if every endomorphism of G is an automorphism. Let F q be …