The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly

Let F be a set of ordered patterns, i.e., graphs whose vertices are linearly ordered. An F-free ordering of the vertices of a graph H is a linear ordering of V (H) such that none of the patterns in F occurs as an induced ordered subgraph. We denote by Ord(F) the decision problem asking whether an input graph admits an F-free ordering; we also use Ord(F) to denote the class of graphs that do adm...

The characterization of distance-regular Cayley graphs originates from the problem identifying strongly regular graphs, or equivalently, partial difference sets. In this paper, a classification on dicyclic groups is obtained. More specifically, it shown that every graph group complete graph, multipartite non-antipodal bipartite with diameter 3 satisfying some additional conditions.

We consider the averaging process on a graph, that is evolution of mass distribution undergoing repeated averages along edges graph at arrival times independent Poisson processes. establish cutoff phenomena for both L1 and L2 distance from stationarity when discrete hypercube complete bipartite. Some general facts about arbitrary graphs are also discussed.

Borowiecki, M. and E. Drgas-Burchardt, Classes of chromatically unique graphs, Discrete Mathematics Ill (1993) 71-75. We prove that graphs obtained from complete equibipartite graphs by deleting some independent sets of edges are chromatically unique. 1. Preliminary definitions and results In this paper we consider finite, undirected, simple and loopless graphs. Two graphs G and H are said to b...

In this paper we introduce and study a type of Cayley graph – subnormal graph. We prove that 2-arc transitive is normal or cover complete bipartite $\mathbf{K}_{p^d,p^d}$ with $p$ prime. Then obtain generic method for constructing half-symmetric (namely edge but not arc transitive) graphs.

In this article we consider graph partitions with prescribed patterns. Specifically a 2-colouring of the vertex set such that one colour induces an independent and other complete bipartite graph. We determine list obstructions (minimal forbidden induced subgraphs) for chordal graphs. This result completes knowledge on minimal 3 × matrix partition problems

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideal...

Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair.

Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair.