Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph T (G) has the triangles of the graph G as its vertices, two of these being adjacent whenever as triangles in G they share an edge. A graph is edge-triangular if every edge is in at least one triangle. ...

This paper investigates a graph enumeration problem, called the maximal Psubgraphs problem, where P is a hereditary or connected-hereditary graph property. Formally, given a graph G, the maximal P-subgraphs problem is to generate all maximal induced subgraphs of G that satisfy P. This problem differs from the wellknown node-deletion problem, studied by Yannakakis and Lewis [1–3]. In the maximal...

The investigation of the graph Gp associated with finite p-groups maximal class was initiated by Blackburn (1958) and became a deep interesting research topic since then. Leedham-Green & McKay (1976–1984) introduced skeletons Gp, described their importance for structural exhibited relation to algebraic number theory. Here we go one step further: partition into so-called Galois trees study gener...

A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) whenever it belongs to P and none of its proper supergraphs of the same order has the property P. A graph is P-extremal if it has a the maximum number of edges among all P-maximal graphs ...

A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which combination of standard true function plus phase term. In this paper, we extend the idea graph (FG) to (CFG). The CFS complexity arises from variety values that its can attain. contrast range expanded plane’s unit circle rather than [0,1]. As result, provides mathematical structure for representing in te...

A maximal independent set is an independent set that is not a proper subset of any other independent set. Liu [J.Q. Liu, Maximal independent sets of bipartite graphs, J. Graph Theory, 17 (4) (1993) 495-507] determined the largest number of maximal independent sets among all n-vertex bipartite graphs. The corresponding extremal graphs are forests. It is natural and interesting for us to consider...

This paper describes tight extended formulations for independent set. The first formulation is for arbitrary independence systems and has size O(n+ μ), where μ denotes the number of inclusion-wise maximal independent sets. Consequently, the extension complexity of the independent set polytope of graphs is O(1.4423). The size O(2n) of the second extended formulation depends on the treewidth tw o...