相关论文: Gutman index of the Mycielskian and its complement
In this paper, we have studied the distance magic labelling of Generalised Mycielskian of a few families of graphs.
In this paper, we define the Mycielskian of a signed graph and discuss the properties of balance and switching in the Mycielskian of a given signed graph. We provide a condition for ensuring the Mycielskian of a balanced signed graph…
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct…
In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph into a new graph which is called the Mycielskian of that graph. In this paper we provide some…
We examine the chromatic index of generalized truncations of graphs and multigraphs.
We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.
We study topological properties of the graph topology.
We show that the homotopy type of the independence complex of the generalized Mycielskian of a graph $G$ is determined by the homotopy type of the independence complex of $G$ and the homotopy type of the independence complex of the…
WE determine the existence of exact (efficient) doubly dominating sets in three famous structures and in their complement for arbitrary graphs.
In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.
The Mycielskian construction, denoted $\mu(G)$, takes a finite simple graph $G$ to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielskian construction, denoted $\mu_t(G)$, takes $G$ to a…
The concept of the \emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\emph{directed graphs by definition}),…
In this paper we investigate a parameter of graphs, called the circular altitude, introduced by Peter Cameron. We show that the circular altitude provides a lower bound on the circular chromatic number, and hence on the chromatic number, of…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
We introduce a modification of the Tur\'an density of ordered graphs and investigate this graph parameter.
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
We are concerned with split graphs and pseudo-split graphs whose complements are isomorphic to themselves. These special subclasses of self-complementary graphs are actually the core of self-complementary graphs. Indeed, we show that all…
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in $\mathbb{R}^5$.