Graph theory experienced a tremendous growth in the 20th century. One of the main
reasons for this phenomenon is the applicability of graph theory in other disciplines such as …

We investigate the effect of the well-known Mycielski construction on the Shannon capacity
of graphs and on one of its most prominent upper bounds, the (complementary) Lovász theta …

The general position problem for graphs was inspired by the no-three-in-line problem from
discrete geometry. A set S of vertices of a graph G is a general position set if no shortest path …

Two graphs of same order are said to be distance equienergetic if their distance energies
are same. In this paper, we rst give a partial insight on the distance spectrum of Mycielskian …

The idea of constructing a triangle-free k-chromatic graphs, where k≥ 3, was initiated in the
middle of the twentieth century. Mycielski who gave a fascinating construction to obtain a …

Graphs serve as mathematical models to analyze many concrete real-world problems
successfully. Certain problems in physics, chemistry, communication science, computer …

The Kirchhoff index and Laplacian-energy-like invariant of a connected graph G, denoted by
Kf (G) and LEL (G), are given by the number of vertex times the sum of the reciprocals of all …

The energy of a graph G, denoted by E (G), is defined as the sum of the absolute values of
all eigenvalues of G. It is proved in [MATCH Commun. Math. Comput. Chem. 79 (2018), 287 …

The Mycielski's construction is a well-known construction on graphs which transforms ak-
chromatic triangle-free graph G into a (k+ 1)-chromatic triangle-free graph μ (G) which is …

The study of Eulerian graphs was initiated in the 18th century and that of Hamiltonian graphs
in the 19th century. These graphs possess rich structures; hence, their study is a very fertile …