Let f(v) denote the maximum number of edges in a graph of order v and of girth at least 5. In this paper, we discuss algorithms for constructing such extremal graphs. This gives constructive lower bounds of f(v) for v ≤ 200. We also provide the exact values of f(v) for v ≤ 24, and enumerate the extremal graphs for v ≤ 10.

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a conne...

Usual graph classes, such as complete graphs, paths, cycles and stars, frequently appear as extremal graphs in graph theory problems. Here we want to turn the reader’s attention to two novel, simply defined, graph classes that appear as extremal graphs in several graph theory problems. We call them bags and bugs. As examples of problems where bags and bugs appear, we show that balanced bugs max...

We observe recent results on the applications of extremal graph theory to cryptography. Classical Extremal Graph Theory contains Erdős Even Circuite Theorem and other remarkable results on the maximal size of graphs without certain cycles. Finite automaton is roughly a directed graph with labels on directed arrows. The most important advantage of Turing machine in comparison with finite automat...