Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we extend the known classification for the |H|...

The objective of this paper is to finds the lower and upper bounds Nordhaus-Gaddum inequalities fuzzy chromatic number for anti-fuzzy graph. This analyzes index complementary anti graphs in some cases. A theorem proved graph be k-critical. Examples are provided derive vertex coloring these graphs.

We prove that any self-complementary graph G contains no proper overfull subgraph H such that (H) = (G) and |V (H)|¡ |V (G)|. Moreover, a self-complementary graph G is overfull if, and only if, it is regular. This is a support for the following conjecture: a self-complementary graph G is Class 2 if; and only if; G is regular. c © 2000 Elsevier Science B.V. All rights reserved. All graphs we con...

In this paper, we propose a family of graph partition similarity measures that take the topology into account. These graph-aware are alternatives to using set not specifically designed for partitions. The two types measures, and shown have opposite behaviors with respect resolution issues provide complementary information necessary assess partitions similar.

In this paper we relate antiblocker duality between polyhedra, graph theory and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, K(G), of the stable set polytope in a graph G and the one associated to its complementary graph, K(Ḡ). We obtain a generalization of the Perfect Graph Theorem proving that the disjunctive indice...

Understanding the relationships between items can improve accuracy and interpretability of recommender systems. Among these relationships, substitute complement attract most attention in e-commerce platforms. The substitutable are interchangeable might be compared with each other before purchasing, while complementary used conjunction usually bought together query item. In this paper, we focus ...

The Gallai and the anti-Gallai graphs of a graph G are complementary pairs of spanning subgraphs of the line graph of G. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph G into the edge sets of the Gallai and anti-Gallai graphs of G. Based on this, an optimal algorithm to find the root graph of a line...