Interval digraphs were introduced by West et all. They can be recognized in polynomial time and admit a characterization in terms of incidence matrices. Nevertheless, they do not have a forbidden structure characterization nor a low-degree polynomial time recognition algorithm. We introduce a new class of ‘adjusted interval digraphs’, obtained by a slight change in the definition. By contrast, ...

We investigate the class of reflexive graphs that admit semilattice polymorphisms, and in doing so, give an algebraic characterisation of chordal graphs. In particular, we show that a graph G is chordal if and only if it has a semilattice polymorphism such that G is a subgraph of the comparability graph of the semilattice. Further, we find a new characterisation of the leafage of a chordal grap...

Programming languages such as CLU, Ada and Modula-3 have included facilities for parametric polymorphism and, more recently, C++ and Java have also added similar facilities. In this paper, we examine the issues of defining denotational semantics for imperative programming languages with polymorphism. We use the framework of reflexive graphs of categories previously developed for a general axiom...

A total k-labeling is a function fe from the edge set to {1, 2, . , ke} and fv vertex {0, 4, 2kv}, where k = max{ke, 2kv}. distance irregular reflexive of graph G k-labeling, if for every two different vertices u 0 G, w(u) 6= w(u ), Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum which has k-labelling called strength denoted by Dref (G). In this paper, we determine exact value some connected graph...

A non-empty set of vertices is called an even dominating set if each vertex in the graph is adjacent to an even number of vertices in the set (adjacency is reflexive). An odd dominating set is defined analogously. Results on parity dominating sets in grid graphs are surveyed and related results on “Lights Out!” games on grids and graphs are discussed.

We introduce the class of bi-arc digraphs, and show they coincide with the class of digraphs that admit a conservative semi-lattice polymorphism, i.e., a min ordering. Surprisingly this turns out to be also the class of digraphs that admit totally symmetric conservative polymorphisms of all arities. We give an obstruction characterization of, and a polynomial time recognition algorithm for, thi...