Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover Q and a stable set cover S s.t. every clique in Q intersects every stable set in S. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (K ̈orner [6]) and graph entropy (Czisz ́ar et al. [5]). Perfect graphs have been recently characterized a...

In this paper we prove that the inductively defined graph dimension has a simple additive property under join operation. The of two graphs is one plus sum dimensions component graphs: $$\mathrm {dim\,} (G_1+ G_2) = 1 +\mathrm G_1+ \mathrm G_2$$ . We use formula to derive an expression for inductive arbitrary finite from its minimum edge clique cover. A corollary any whose maximal cliques are al...

The problem of nding the minimum topology of multipro-cessing substrates supporting parallel execution of any given neighbourhood constrained system is proposed and possible optimal strategies are investigated based on the relationship between Barbosa's scheduling by edge reversal-SER-distributed algorithm and the minimum clique covering problem. It is shown that from any given clique covering ...

Imbalance is a classical graph layout problem with several applications, particularly in drawing. The imbalance of σ determined by how well-balanced the neighbors vertices are σ. In present work, we study parameterized twin cover graph. We show that XP cover, and FPT when size largest clique outside cover. contrast, introduce notion succinct representations graphs terms their demonstrate NP-har...

We study the min-max problem in factor graphs, which seeks the assignment that minimizes the maximum value over all factors. We reduce this problem to both min-sum and sum-product inference, and focus on the later. In this approach the min-max inference problem is reduced to a sequence of Constraint Satisfaction Problems (CSP), which allows us to solve the problem by sampling from a uniform dis...

A graph is (H1,H2)-free for a pair of graphsH1, H2 if it contains no induced subgraph isomorphic toH1 orH2. In 2001, Král’, Kratochvíl, Tuza, and Woeginger initiated a study into the complexity of Colouring for (H1,H2)free graphs. Since then, others have tried to complete their study, but many cases remain open. We focus on those (H1,H2)-free graphs where H2 is H1, the complement of H1. As thes...

A graph is (H1,H2)-free for a pair of graphsH1, H2 if it contains no induced subgraph isomorphic toH1 orH2. In 2001, Král’, Kratochvíl, Tuza, and Woeginger initiated a study into the complexity of Colouring for (H1,H2)free graphs. Since then, others have tried to complete their study, but many cases remain open. We focus on those (H1,H2)-free graphs where H2 is H1, the complement of H1. As thes...

Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each vertex represents the side information availability to that user. The aim is to find an encoding to minimum number of bits (optimal rate) that, when broadca...

Contagion processes have been proven to fundamentally depend on the structural properties of interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections all-to-all pair-wise interactions (cliques) and/or group interactions, involving many their members at once. In this work, focusing structures represented as simp...