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In this paper we introduce the concept of skew-quotient of Randić and sumconnectivity energy of directed graphs. We then obtain upper and lower bounds for skew-quotient of Randić and sum-connectivity energy of digraphs. Then, we compute the skewquotient of Randić and sum-connectivity energy of some graphs such as star digraph, complete bipartite digraph, the Sm ... P2 digraph and a crown digraph. [ABSTRACT FROM AUTHOR]

Representing a set of vertices in a graph means of a matrix was introduced by E. Sampath Kumar. Let G(V,E) be a graph and S ⊆ V be a set of vertices. We can represent the set S by means of a matrix as follows, in the adjacency matrix A(G) of G replace the aii element by 1 if and only if, vi ∈ S. In this paper we study the special case of set S being dominating set and corresponding domination energy of some class of graphs. [ABSTRACT FROM AUTHOR]

Representing a subset of vertices in a graph by means of a matrix was introduced by E. Sampath Kumar. Let G(V, E) be a graph and S ⊆ V be a set of vertices. We can represent the set S by means of a matrix as follows, in the adjacency matrix A(G) of G replace the aii element by 1 if and only if, vi ∊ S. In this paper we study the set S being dominating set and corresponding domination energy of some class of graphs. [ABSTRACT FROM AUTHOR]

Graph labeling where vertices and edges are assigned values subject to certain conditions have been motivated by various applied mathematical fields. Most of the problems in graph labeling are discussed on undirected graphs. Bloom G.S. and Hsu D.F. defined the labeling on directed graphs. In this paper, we discuss the adjacency matrices of graceful digraphs such as unidirectional paths, alternating paths, many orientations of directed star and a class of directed bistar. We also discuss the adjacency matrices of unidirectional paths and alternating paths if they are odd digraceful. [ABSTRACT FROM AUTHOR]

Representation of a set of vertices in a graph by means of a matrix was intro- duced by Sampath Kumar. Let G(V,E) be a graph and S ⊆ V be a set of vertices, we can represent the set S by means of a matrix as follows, in the adjacency matrix A(G) of G replace the aii element by 1 if and only if vi ϵ S. In this paper we define set energy and find its properties and also study the special case of set S being a dominating set and corresponding domination energy of some special class of graphs. [ABSTRACT FROM AUTHOR]