The extremal graphs $\mathrm {EX}(n,\mathcal F) $ and spectral extremal graphs $\mathrm
{SPEX}(n,\mathcal F) $ are the sets of graphs on $ n $ vertices with maximum number of …

Given a family F of graphs, a graph G is called F-free if G contains none of F as its subgraph.
The following problem is one of the most concerned problems in spectral extremal graph …

Let $\mathcal {G}=\{G_1,\ldots, G_n\} $ be a family of graphs of order $ n $ with the same
vertex set. A rainbow Hamiltonian cycle in $\mathcal {G} $ is a cycle that visits each vertex …

Let G be a simple connected graph with vertex set V (G). The matching polynomial of G is
defined as MG (x)=∑ k= 0 n∕ 2 (− 1) km (G, k) xn− 2 k, where m (G, k) denotes the number …

A graph transformation called the compression of a graph G is known to decrease the
number of spanning trees, the all-terminal reliability, and the magnitude of the coefficients of …

Let $ G $ be a simple graph with no even cycle, called an odd-cycle graph. Cavers et
al.[Cavers et al. Skew-adjacency matrices of graphs, Linear Algebra Appl. 436 (2012), 4512 …

Given a simple graph G and vertices u, v∈ V (G), let NG (u) and NG (v) denote the
neighborhoods in G of u and v respectively. The compression of G from u to v produces a …

Kelmans, and later independently Bogdanowicz and Satyanarayana, Schoppmann, and
Suffel, showed that a graph operation which has come to be known as the compression of G …

Abstract Dr. Charles L. Suffel (1941–2021) was an influential mathematics educator and
scholar at Stevens Institute of Technology for more than half a century. The Managing Editor …

In the center of this thesis graph polynomials and graph transformations stand, their role in
algebraic and extremal graph theory. In the first half of this thesis we give a survey about the …