Laplacian Spectra of Semigraphs

Consider a semigraph $G=(V,\,E)$; in this paper, we study the eigenvalues of the Laplacian matrix of $G$. We show that the Laplacian of $G$ is positive semi-definite, and $G$ is connected if and only if $\lambda_2 >0.$ Along the similar lines of graph theory bounds on the largest eigenvalue, we obtain upper and lower bounds on the largest Laplacian eigenvalue of G and enumerate the Laplacian eigenvalues of some special semigraphs such as star semigraph, rooted 3-uniform semigraph tree.Comment: 18 pages, 3 figure

Domination number of a bipartite semigraph when it is a cycle

Semigraph is a generalization of graph, with two or more vertices on edges which allows multiplicity in every concept of graph when it comes to semigraph. When number of vertices on the edges are restricted to two the semigraph is a graph, so every graph is a semigraph. In this article we deal with the variety of bipartite semigraphs, namely bipartite, s-bipartite and e-bipartite and bounds for their domination number (adjacent domination number and end vertex adjacent domination number) in particular when the semigraph is a cycle and also about possible size of the bipartite sets when the bipartite semigraph is a cycle.Publisher's Versio

Deoxyribonucleic acid (DNA) splicing system from graph theoretic perspective

In 1987, Head introduced the recombinant process of deoxyribonucleic acid (DNA) splicing system through a framework of Formal Language Theory. To express this phenomenon, a comprehensive writing system of the rule sets, proper terms and definitions pioneerly introduced by Head. The analysis on the recombinant behavior of double-stranded DNA molecules, characteristics and various type of splicing systems has sparks the researcher to explore more splicing mechanism extensively. The aim of this paper is to give an exhaustive review on the application of graph in DNA splicing system

Graph splicing rules with cycle graph and its complement on complete graphs

Graph splicing system is a notion originally used to illustrate the one-dimensional string of DNA splicing in the form of a graph. A graph splicing system is associated with a graph splicing scheme where graph splicing rules are defined. A graph splicing rule restricts the possible cuts to occur on the edges of the initial graph(s) in a graph splicing system. The subgraphs of the initial graph are used in the splicing rules to determine the edges that will be cut from the initial graph. The concept of graph splicing system can be applied on various types of graph, hence generates components of spliced graphs depending on the types of the graph splicing rules used. There is a graph splicing rule called as a cutting rule which can be applied on both linear graphs and circular graphs where the graphs are transformed into Pseudo-Linear Form. However, this cutting rule has limited various possible cuts that can occur on the complete graph. Therefore, in this research, the original concept of graph splicing system is applied on complete graphs as the initial graphs. Also, graph splicing rules involving subgraphs of the initial graphs which are also complete graphs, are considered and applied in the graph splicing system. Furthermore, the generated spliced graphs are obtained through the graph splicing system