For n ≥ 3, let (Hn, E) denote the n-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on n vertices. We show that for all structures Γ with domain Hn whose relations are first-order definable in (Hn, E) the constraint satisfaction problem for Γ is either in P or is NP-complete. We moreover sho...

Let Γ = (V,E) be a point-symmetric reflexive relation and let v ∈ V such that |Γ(v)| is finite (and hence |Γ(x)| is finite for all x , by the transitive action of the group of automorphisms). Let j ∈ N be an integer such that Γ(v)∩Γ(v) = {v}. Our main result states that |Γ(v)| ≥ |Γ(v)|+ |Γ(v)| − 1. As an application we have |Γ(v)| ≥ 1+(|Γ(v)|−1)j. The last result confirms a recent conjecture of...

Correspondence homomorphisms are both a generalization of standard homomorphisms and a generalization of correspondence colourings. For a fixed target graph H, the problem is to decide whether an input graph G, with each edge labeled by a pair of permutations of V (H), admits a homomorphism to H ’corresponding’ to the labels, in a sense explained below. We classify the complexity of this proble...

Veldkamp polygons are certain graphs ?=(V,E) such that for each v?V, ?v is endowed with a symmetric anti-reflexive relation ?v. These relations all trivial if and only ? thick generalized polygon. A polygon called flat no two vertices have the same set of opposite in natural sense. We explore connection between quadrangles polar spaces. Using this connection, we give complete classification whi...

In this note, we study maximal monotonicity of linear relations (set-valued operators with linear graphs) on reflexive Banach spaces. We provide a new and simpler proof of a result due to BrézisBrowder which states that a monotone linear relation with closed graph is maximal monotone if and only if its adjoint is monotone. We also study Fitzpatrick functions and give an explicit formula for Fit...

Let Γ = (V,E) be a reflexive relation with a transitive automorphisms group. Let v ∈ V and let F be a finite subset of V with v ∈ F. We prove that the size of Γ(F ) (the image of F ) is at least |F |+ |Γ(v)| − |Γ−(v) ∩ F |. Let A,B be finite subsets of a group G. Applied to Cayley graphs, our result reduces to following extension of the Scherk-Kemperman Theorem, proved by Kemperman: |AB| ≥ |A|+...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

This paper continues the investigation of logic competing theories (be they scientific, social, political etc.) initiated in [4]. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Ploščica's representation general lattices. axiomatize resulting non-distributive these structures and prove completeness th...