We study the joint components in a random 'double graph' that is obtained by superposing red and blue binomial graphs on $n$~vertices. A component maximal set of vertices supports both spanning tree. show there are critical pairs edge densities at which giant appears. In contrast to standard graph model, phase transition first order: size largest jumps from $O(1)$ $\Theta(n)$ point. connect thi...

A vertex coloring of a graph $G$ is called distinguishing if no non-identity automorphisms can preserve it. The number $G$, denoted by $D(G)$, the minimum colors required for such coloring, and threshold $\theta(G)$, $k$ that every $k$-coloring distinguishing. As an alternative definition, $\theta(G)$ one more than maximum cycles in cycle decomposition $G$. In this paper, we characterize $\thet...

Numerous studies have revealed various working memory (WM)-related brain activities that originate from various cortical regions and oscillate at different frequencies. However, multi-frequency band analysis of the brain network in WM in the cortical space remains largely unexplored. In this study, we employed a graph theoretical framework to characterize the topological properties of the brain...

A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). Circular-perfect graphs form a well-studied superclass of perfect graphs. We extend the above result for perfect graphs by showing that clique and chromatic number of a circularperfect graph are computable in polynomial time...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edgebandwidth is at least as large as bandwidth for every graph, with equality for certain caterpillars. We obtain sharp or nearly sharp bounds on the change in edge-bandwidth under addition, subdivision, or contracti...

The theta function of a graph, also known as the Lovv asz number, has the remarkable property of being computable in polynomial time, despite being \sandwiched" between two hard to compute integers, i.e., clique and chromatic number. Very little is known about the explicit value of the theta function for special classes of graphs. In this paper we provide the explicit formula for the Lovv asz n...

The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovász theta function play an important role in zero-error communication. In this paper, we show that the Lovász theta function is an upper bound ...

We introduce a unifying generalization of the Lovász theta function, and the associated geometric embedding, for graphs with weights on both nodes and edges. We show how it can be computed exactly by semidefinite programming, and how to approximate it using SVM computations. We show how the theta function can be interpreted as a measure of diversity in graphs and use this idea, and the graph em...