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 …

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 …

Let $\chi (G) $ denote the chromatic number of a graph and $\chi_v (G) $ denote the vector
chromatic number. For all graphs $\chi_v (G)\le\chi (G) $ and for some graphs $\chi_v …

A vector t-coloring of a graph is an assignment of real vectors p_1, ..., p_n p 1,…, pn to its
vertices such that p_i^ Tp_i= t-1, pi T pi= t-1, for all i= 1, ..., ni= 1,…, n and p_i^ Tp_j ≤-1 pi T …

The orthogonal rank of a graph $ G=(V, E) $ is the smallest dimension $\xi $ such that there
exist non-zero column vectors $ x_v\in\mathbb {C}^\xi $ for $ v\in V $ satisfying the …

We prove that if G and H are primitive strongly regular graphs with the same parameters and
ϕ is a homomorphism from G to H, then ϕ is either an isomorphism or a coloring …

We study equality in the Hoffman bound for the chromatic number and Hoffman colorings in
regular and irregular graphs. We investigate the connection between Hoffman colorability …

We prove that if G and H are primitive strongly regular graphs with the same parameters and
ϕ is a homomorphism from G to H, then ϕ is either an isomorphism or a coloring …

A graph homomorphism is a function between the vertex set of two graphs which maps pairs
of adjacent vertices to pairs of adjacent vertices. Many graph parameters can be expressed …

An embedding i↦ pi∈ R d of the vertices of a graph G is called universally completable if the
following holds: For any other embedding i↦ qi∈ R k satisfying qi T qj= pi T pj for i= j and i …