A $P_4$-free graph is called a cograph. In this paper we partially characterize finite groups whose power As will see, problem generalization of the determination in which every element has prime order, first raised by Graham Higman 1957 and fully solved very recently. First determine all $G$ $H$ for $G\times H$ We show that cograph can be characterised condition only involving elements orders ...

Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with n vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consecutive outputs) is O(n). The time needed to generate the first output is also O(n), which gives an ove...

In this work, we attempt to establish recognition properties and characterization for two classes of perfect graphs, namely cographs and threshold graphs, leading to constant-time parallel recognition algorithms. We classify the edges of an undirected graph as either free, semi-free or actual, and define the class of A-free graphs as the class containing all the graphs with no actual edges. The...

In this paper, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this work, we present necessary and sufficient conditions for the controllability of cographs, and provide an efficient method for selecting a minimal set of input nodes from which the network is ...

The slope variety of a graph is an algebraic set whose points correspond to drawings of that graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path. We construct a bijection between the zeroes of the slope variety of the complete graph on n vertices over F2, and the complementreducible graphs on n vertices.

Kotovsky and Gentner (1996) showed that presenting progressively aligned examples helped children discover relational similarities: Comparisons based on initially concrete and highly similar, but progressively more abstract exemplars helped the discovery of higher-order relational similarities. We investigated whether progressive alignment can aid learning of relational categories with either a...

In this article, the extremal structures for the mean order of connected induced subgraphs of cographs are determined. It is shown that among all connected cographs of order n ≥ 7, the star K1,n−1 has maximum mean connected induced subgraph order, and for n ≥ 3, the n-skillet, K1+(K1∪Kn−2), has minimum mean connected induced subgraph order. It is deduced that the density for connected cographs ...

We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of monadic second-order logic: one where we can only quantify over sets of vertices and one where we can also quantify over sets of edges. For several special cas...

Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B| = b and |W| = w such that no vertex in B is adjacent to any vertex inW. In this paper we show that the problem is polynomial when restricted to cographs, distance-hereditary graphs, interval graphs and strongly chordal graphs. We show that the problem is NP-c...