In this paper, we define irregular interval-valued fuzzy graphs and their various classifications. Size of regular interval-valued fuzzy graphs is derived. The relation between highly and neighbourly irregular interval-valued fuzzy graphs are established. Some basic theorems related to the stated graphs have also been presented.

Interval graphs have engaged the interest of researchers for over twenty-five years. The scope of current research in this area now extends to the mathematical and algorithmic properties of interval graphs, their generalizations, and graph parameters motivated by them. One main reason for this increasing interest is that many real-world applications involve solving problems on graphs which are ...

A graph is an interval graph if it is the intersection graph of intervals on a line. Interval graphs are known to be the intersection of chordal graphs and asteroidal triple-free graphs, two families where the well-known Lexicographic Breadth First Search (LBFS) plays an important algorithmic and structural role. In this paper we show that interval graphs have a very rich LBFS structure and tha...

We study the paired-domination problem on interval graphs and circular-arc graphs. Given an interval model with endpoints sorted, we give an O(m + n) time algorithm to solve the paired-domination problem on interval graphs. The result is extended to solve the paired-domination problem on circular-arc graphs in O(m(m+ n)) time. MSC: 05C69, 05C85, 68Q25, 68R10, 68W05

Scale free graphs have attracted attention by their non-uniform structure that can be used as a model for various social and physical networks. In this paper, we propose a natural and simple random model for generating scale free interval graphs. The model generates a set of intervals randomly under a certain distribution, which defines a random interval graph. The main advantage of the model i...

Interval graphs—the intersection graphs of one dimensional intervals—are considered one of the most useful mathematical structures to model real life applications [18]. Interval graphs have been widely studied since they first appeared in the literature in 1957. In 1976, Booth and Lueker [7] introduced a data structure called PQ-trees that could recognize interval graphs in linear time; since t...