On hypergraphs with every four points spanning at most two triples.
On hyper-Zagreb index conditions for hamiltonicity of graphs
During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to be Hamilton-connected....
On idempotent binary relations on a finite set
On identifying codes in the King grid that are robust against edge deletions.
On imbalances in digraphs
On improper interval edge colourings
We study improper interval edge colourings, defined by the requirement that the edge colours around each vertex form an integer interval. For the corresponding chromatic invariant (being the maximum number of colours in such a colouring), we present upper and lower bounds and discuss their qualities; also, we determine its values and estimates for graphs of various families, like wheels, prisms or complete graphs. The study of this parameter was inspired by the interval colouring, introduced by...
On incidence algebras and directed graphs.
On Incidence Structures in Finite Classical Groups.
On 𝓕-independence in graphs
Let be a set of graphs and for a graph G let and denote the maximum order of an induced subgraph of G which does not contain a graph in as a subgraph and which does not contain a graph in as an induced subgraph, respectively. Lower bounds on and are presented.
On independent sets
On independent sets and non-augmentable paths in directed graphs
We investigate sufficient conditions, and in case that D be an asymmetrical digraph a necessary and sufficient condition for a digraph to have the following property: "In any induced subdigraph H of D, every maximal independent set meets every non-augmentable path". Also we obtain a necessary and sufficient condition for any orientation of a graph G results a digraph with the above property. The property studied in this paper is an instance of the property of a conjecture of J.M. Laborde, Ch. Payan...
On independent vertices and edges of belt graphs.
On infinite outerplanar graphs
In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs.
On infinite tournaments with regular automorphism groups.
On infinite uniquely partitionable graphs and graph properties of finite character
A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property is of finite character if a graph G has a property if and only if every finite induced subgraph of G has a property . Let ₁,₂,...,ₙ be graph properties of finite character, a graph G is said to be (uniquely) (₁, ₂, ...,ₙ)-partitionable if there is an (exactly one) partition V₁, V₂, ..., Vₙ of V(G) such that for i = 1,2,...,n. Let us denote by ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ the class of all (₁,₂,...,ₙ)-partitionable...
On information storage and retrieval systems
On integer sequences associated with the cyclic and complete graphs.
On integer-sequence-based constructions of generalized Pascal triangles.
On integral sum graphs with a saturated vertex
As introduced by F. Harary in 1994, a graph is said to be an if its vertices can be given a labeling with distinct integers so that for any two distinct vertices and of , is an edge of if and only if for some vertex...
On interval graphs and matrice profiles