This paper utilizes an extremely simple idea: in the multiplicative group of a finite field $F_q$, cosets of a certain subgroup are considered, and an attempt is made to combine these cosets into pairs such that the resulting induced subgraph in the corresponding Paley graph is strongly regular. It is shown that there exists an infinite sequence of Paley graphs that can be partitioned into Petersen graphs in this manner. Furthermore, a new strongly regular graph with parameters $(50, 21, 8, 9)$ is constructed using this method.
We show, under a certain assumption, that the Cheeger constant of a connected Cayley graphon is bounded from above in terms of its bipartiteness ratio, and also in terms of the gap between the top of the spectrum of its Laplacian and $2$. Using this result, we prove that if a connected Cayley graphon $C(G,\gamma)$ is b...
We use a Gröbner basis technique first introduced by Knutson, Miller and Yong to study the interplay between properties of a graph [Formula: see text] and algebraic properties of the toric ideal that it defines. We first recover a well-known height formula for the toric ideal of a graph [Formula: see text] and demonstr...
Sergio Da Silva, Emma Naguit, Jenna Rajchgot· Journal of Algebra and its A...· 0 citations
How large of a minimum degree does an $n$-vertex graph need before we are sure that it contains a perfect matching? Dirac's theorem states that a graph on an even number of vertices in which each vertex has degree at least $n/2$ has this property. In this short expository note, intended to be used in the classroom, we...
An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|E|}, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated th...
Gr'egoire Beaudoire, C. Bentz, C. Picouleau· 0 citations
A graph is
perfect
if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independen...
We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ \omega(\AG(R_4))=5<6=\chi(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behb...
R. Nikandish· 0 citations
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