Related papers: A class of reconstructible graphs

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.

In the present paper we construct a one-to-one correspondence between the set of graph-knots and the set of homotopy classes of looped graphs. Moreover, the graph-knot and the homotopy class constructed from a given knot are related with…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed…

This paper investigates some combinatorial and algebraic properties of a Witt type formula for graphs.

This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a…

It is shown that shift graphs can be realized as disjointness graphs of 1-intersecting curves in the plane. This implies that the latter class of graphs is not $\chi$-bounded.

Dotted graphs are certain finite graphs with vertices of degree 2 called dots in the $xy$-plane $\mathbb{R}^2$, and a dotted graph is said to be admissible if it is associated with a lattice polytope in $\mathbb{R}^2$ each of whose edge is…

We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…

In this paper has been proved the pluripolarity of graphs of algebroid functions

In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…

This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…

The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…

We describe computer searches that prove the graph reconstruction conjecture for graphs with up to 13 vertices and some limited classes on larger sizes. We also investigate the reconstructibility of tournaments up to 13 vertices, digraphs…

In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.

For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…

We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.