Related papers: Rhomboidal C4C8 toris which are Cayley graphs
Suppose that $R$ is a finite commutative ring with identity. The involutory Cayley graph $\G(R)$ of $R$ is the graph whose vertices are the elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $(x-y)^2=1$. In…
A rectangular dual of a plane graph $G$ is a contact representation of $G$ by interior-disjoint rectangles such that (i) no four rectangles share a point, and (ii) the union of all rectangles is a rectangle. In this paper, we study…
The unitary Cayley graph $C_R$ of a finite unital ring $R$ is the simple graph with vertex set $R$ in which two elements $x$ and $y$ are connected by an edge if and only if $x-y$ is a unit of $R$. We characterize the unitary Cayley graph…
In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some…
In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of…
A nut graph is a non-trivial simple graph such that its adjacency matrix has a one-dimensional null space spanned by a full vector. It was recently shown by the authors that there exists a $d$-regular circulant nut graph of order $n$ if and…
A circulant is a Cayley graph over a cyclic group. A well-covered graph is a graph in which all maximal stable sets are of the same size, or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and…
In a recent paper (arXiv:1505.01475 ) Est\'elyi and Pisanski raised a question whether there exist vertex-transitive Haar graphs that are not Cayley graphs. In this note we construct an infinite family of trivalent Haar graphs that are…
Honeycomb toroidal graphs are trivalent Cayley graphs on generalized dihedral groups. We examine the two historical threads leading to these graphs, some of the properties that have been established, and some open problems.
This paper deals with triangulations of the 2-torus with the vertex labeled general octahedral graph $O_4$ which is isomorphic to the complete four-partite graph $K_{2,2,2,2}$; it is known that there exist precisely twelve such…
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with…
A link diagram can be considered as a $4$-valent graph embedded in the $2$-sphere and divides the sphere into complementary regions. In this paper, we show that any link has a diagram with only triangles and quadrilaterals. This extends…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.
Cayley graphs are graphs on algebraic structures, typically groups or group-like structures. In this paper, we have obtained a few results on Cayley graphs on Cyclic groups, powers of cycles, Cayley graphs on some non-abelian groups, and…
This paper aims to determine the ring structure of the torus equivariant cohomology of odd-dimensional complex quadrics by computing the graph equivariant cohomology of their corresponding GKM graphs. We show that its graph equivariant…
We introduce a family of graphs that generalises the class of Cayley graphs. For non-empty subsets L, R of a group G, the two-sided Cayley graph 2SC(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if…
We construct a polynomial-time algorithm that given a graph $X$ with $4p$ vertices ($p$ is prime), finds (if any) a Cayley representation of $X$ over the group $C_2\times C_2\times C_p$. This result, together with the known similar result…
Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide…
We consider a polynomial version of the Cayley numbers. Namely, we define the ring of Cayley polynomials in terms of generators and relations in the category of alternative algebras. The ring turns out to be an octonion algebra over an…
The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. Using a computer, we determine when the…