Related papers: List of constructions of $NO^+(6,2)$

In this note, we give an alternative construction of the $G_2(2)$-graph from a $U_3(2)$-geometry.

Let $Q^{+}(2n-1,2)$ be a non-degenerate hyperbolic quadric of $PG(2n-1,2)$. Let $NO^{+}(2n,2)$ be the tangent graph, whose vertices are the points of $PG(2n-1,2) \setminus Q^{+}(2n-1,2)$ and two vertices $u,~v$ are adjacent if the line…

We prove the switching equivalence of the strongly regular polar graphs $NO^\pm(4m,2)$, $NO^\mp(2m+1,4)$, and $\Gamma(O^\mp(4m,2))$ plus an isolated vertex by giving an analytic description for them and their associated two-graphs.

In this note, we give an alternative and explicit construction of the $G_2(2)$-hexagon from a $U_3(2)$-geometry.

There are two particular $\Theta_6$-graphs - the 6-cycle graphs with a diagonal. We find the planar Tur\'an number of each of them, i.e. the maximum number of edges in a planar graph $G$ of $n$ vertices not containing the given $\Theta_6$…

In this paper, we present an iterative construction of a polar code and develop properties of the dual of a polar code. Based on this approach, belief propagation of a polar code can be presented in the context of low-density parity check…

We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erd\H{o}s. We also mention some related problems.

We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings' theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws…

We construct minor-closed addable families of graphs that are subcritical and contain all planar graphs. This contradicts (one direction of) a well-known conjecture of Noy.

This paper proves that for each positive integer $m$, there is a planar graph $G$ which is not $(4m+\lfloor \frac{2m-1}{9}\rfloor,m)$-choosable. Then we pose some conjectures concerning multiple list colouring of planar graphs.

A conjecture regarding the structure of expander graphs is discussed.

We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…

We construct a planar graph with twin-width equal to seven.

In this paper, we give a method to construct non-symmetric association schemes of class $3$ from non-symmetric association schemes of class $2$. This construction is a non-symmetric analogue of the construction of Taylor graphs as an…

This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs.

We produce a new, shorter construction of a minor-universal planar graph.

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real…

We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$-tight surface graphs in the case of the sphere, the plane, the twice punctured sphere and the torus. In…

In the present note we use rank-2-bundles over ${\bb P}^3$ to construct octic hypersurfaces with many nodes. We give an example with 128 nodes.

In this paper, we give several constructions for the pairs of graphs to be equienergetic and Randic' equienergetic graphs. Also, some new families of integral and Randic' integral graphs are obtained. As an application, a sequence of graphs…