When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

Intersection graphs provide theory to underlie much of graph theory. They epitomize graph-
theoretic structure and have their own distinctive concepts and emphasis. They subsume …

In this study, the notions of picture fuzzy ϕ-tolerance competition graphs are exhibited
adding more uncertainties to the fuzzy ϕ-tolerance competition graphs. Taking ϕ as max …

Any given graph can be embedded in a chordal graph by adding edges, and the resulting
chordal graph is called a triangulation of the input graph. In this paper we study minimal …

The study of algorithmic graph theory and structured families of graphs is an important
branch of discrete mathematics. It finds numerous applications, from data transmission …

An independent set of three vertices such that each pair is joined by a path that avoids the
neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT …

We define trapezoid graphs, an extension of both interval and permutation graphs. We show
that this new class properly contains the union of the two former classes, and that trapezoid …

Semiorders may form the simplest class of partially ordered sets that accommodate
thresholds of discriminability in binary comparisons. Many other classes of ordered sets that …

In this paper, intuitionistic fuzzy tolerance graphs and intuitionistic fuzzy ϕ ϕ-tolerance
graphs are defined and investigated several interesting properties. Here ϕ ϕ is any real …

In this paper, fuzzy ϕ ϕ-tolerance competition graphs are defined. Several interesting
properties are investigated. Here ϕ ϕ is any real valued function. Particular cases of ϕ ϕ …