Corona Of Graphs Research Articles

On Strong Resolving Domination in the Join and Corona of Graphs

Let G be a connected graph. A subset S \subseteq V(G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u,v \in V(G), there exists a vertex w \in S such that u \in I_G[v,w] or v \in I_G[u,w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G. In this paper, we characterize the strong resolving dominating sets in the join and corona of graphs and determine the bounds or exact values of the strong resolving domination number of these graphs.

Fair Secure Dominating Set in the Corona of Graphs

Fair Secure Dominating Set in the Corona of Graphs

On cocoloring of corona of graphs

On cocoloring of corona of graphs

Resistance distances in corona and neighborhood corona networks based on Laplacian generalized inverse approach

Let [Formula: see text] and [Formula: see text] be two graphs on disjoint sets of [Formula: see text] and [Formula: see text] vertices, respectively. The corona of graphs [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the graph formed from one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text] where the [Formula: see text]th vertex of [Formula: see text] is adjacent to every vertex in the [Formula: see text]th copy of [Formula: see text]. The neighborhood corona of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the graph obtained by taking one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text] and joining every neighbor of the [Formula: see text]th vertex of [Formula: see text] to every vertex in the [Formula: see text]th copy of [Formula: see text] by a new edge. In this paper, the Laplacian generalized inverse for the graphs [Formula: see text] and [Formula: see text] is investigated, based on which the resistance distances of any two vertices in [Formula: see text] and [Formula: see text] can be obtained. Moreover, some examples as applications are presented, which illustrate the correction and efficiency of the proposed method.

On the fractional matching number of the join and corona of graphs

On the fractional matching number of the join and corona of graphs

Perfect Outer-connected Domination in the Join and Corona of Graphs

Perfect Outer-connected Domination in the Join and Corona of Graphs

Combinatorial Approach in Counting the Balanced Bicliques in the Join and Corona of Graphs

Combinatorial Approach in Counting the Balanced Bicliques in the Join and Corona of Graphs

Diophantine Edge Graceful Graph

Background: Graph labeling problems have interesting applications in coding theory, communication networks, optimal circuits’ layouts and graph decomposition problems, as described in various patents. Keywords: Diophantine edge graceful, complete (m, h) trees, corona of graphs.

Restrained independent 2-domination in the join and corona of graphs

Restrained independent 2-domination in the join and corona of graphs

On injective chromatic polynomials of graphs

The injective chromatic number χi(G) [G. Hahn, J. Kratochvil, J. Siran and D. Sotteau, On the injective chromatic number of graphs, Discrete Math. 256(1–2) (2002) 179–192] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. The nature of the coefficients of injective chromatic polynomials of complete graphs, wheel graphs and cycles is studied. Injective chromatic polynomial on operations like union, join, product and corona of graphs is obtained.

Restrained weakly convex domination in the join and corona of graphs

In this paper, we explore the concept of restrained weakly connected domination in graphs. In particular, we characterized the restrained weakly connected dominating sets in the join and corona of graphs and as a consequence, their restrained weakly connected domination numbers are obtained. A connected graph is constructed with a given order, weakly connected domination number, and restrained weakly connected domination number.

Restrained weakly connected domination in the join and corona of graphs

In this paper, we explore the concept of restrained weakly connected domination in graphs. In particular, we characterized the restrained weakly connected dominating sets in the join and corona of graphs and as a consequence, their restrained weakly connected domination numbers are obtained. A connected graph is constructed with a given order, weakly connected domination number, and restrained weakly connected domination number.

Isolate domination in the join and corona of graphs

Isolate domination in the join and corona of graphs

Secure weakly connected domination in the corona of graphs

Secure weakly connected domination in the corona of graphs

Clique cover of the join and the corona of graphs

Clique cover of the join and the corona of graphs

Secure weakly convex domination in the join and corona of graphs

Secure weakly convex domination in the join and corona of graphs

Secure convex dominating sets in corona of graphs

Secure convex dominating sets in corona of graphs

Tree cover of the join and the corona of graphs

Tree cover of the join and the corona of graphs

Independent non-split domination in the join and corona of graphs

Independent non-split domination in the join and corona of graphs

Signed qRoman k-domination number of the join and corona of graphs

Signed qRoman k-domination number of the join and corona of graphs