In this paper, we introduce a class of double coset cayley digraphs induced by right solvable ward groupoids. These class of graphs can be viewed as a generalization of double coset cayley graphs induced by groups. Further, many graph properties are expressed in terms of algebraic properties.

We give a geometric description of the free double category generated by a double reflexive graph. Its cells are homotopy classes of colourings of certain rectangular complexes in the plane. A number of examples illustrate the wide variety of combinatorial properties of the plane this touches.

In a graph G = (V, E) , a vertex dominates itself and all its neighbors. A double dominating set of G is a dominating set that dominates every vertex of G at least twice. In this paper, we characterize vertices that are in all or in no minimum double dominating sets in trees.

In this paper we introduce a new class of double coset Cayley digraphs induced by loops. These graphs can be considered as the generalization of Double coset Cayley digraphs induced by groups . Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature. Mathematics Subject Classification: 05C25

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every vertex x ∈ V (G). In the paper we introduce a closure concept for 1-Hamiltonconnectedness in claw-free graphs. If G is a (new) closure of a claw-free graph G, then G is 1-Hamilton-connected if and only if G is 1-Hamilton-connected, G is the line graph of a multigraph, and for some x ∈ V (G), G − x is the line graph of a ...

In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of p...

In a recent paper, mimicking Winskel's construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of p...

Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of endowed with a bracket. In this work, we provide study morphisms double algebras, which relate to the $H_0$-Poisson structures Crawley-Boevey. We prove in particular that algebra structure defined for an arbitrary quiver only depends upon seen undirected graph, up isomorphism. derive from our result...

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the annihilating-ideal graph of a commutative ring $r$ is denoted by $ag(r)$, whose vertices are all nonzero ideals of $r$ with nonzero annihilators and two distinct vertices $i$ and $j$ are adjacent if and only if $ij=0$. in this article, we completely characterize rings $r$ when $gr(ag(r))neq 3$.