Computing Gutman Connection Index of Thorn Graphs

Chemical structural formula can be represented by chemical graphs in which atoms are considered as vertices and bonds between them are considered as edges. A topological index is a real value that is numerically obtained from a chemical graph to predict its various physical and chemical properties. Thorn graphs are obtained by attaching pendant vertices to the different vertices of a graph under certain conditions. In this paper, a numerical relation between the Gutman connection (GC) index of a graph and its thorn graph is established. Moreover, the obtained result is also illustrated by computing the GC index for the particular families of the thorn graphs such as thorn paths, thorn rods, thorn stars, and thorn rings.

Topological Indices of Some Classes of Thorn Complete and Wheel Graphs

We have multiple real numbers that describe chemical descriptors in the field of Graph theory. These descriptors constitute the entire structure of a graph, which possesses an actual chemical structure. Among these, the main focus of topological indices is that they are associated with many non-identical physiochemical properties of chemical compounds. Also, the biological properties of chemical compounds can be established by the topological indices. In this analysis, we compute the Reciprocal Randic index〖(R〗^(-1)), Reduced Reciprocal Randic index(〖RR〗^(-1)), Atom-bond Connectivity index(ABC) and the geometric arithmetic index(GA) of thorn graphs are obtained theoretically.

On the Vertex Multiplication Graphs

For any graph , with vertex set { } and a p-tuble of positive integers , the vertex multiplication graph is defined as the graph with vertex set consists of copies of each , where the copies of and are adjacent in if and only if the corresponding vertices and are adjacent in G . In this paper, we prove that the spectrum of is same as that of spectrum of its quotient graph with additional zero eigenvalues with multiplicity , where . Also we prove that the determinant of is minimum for and maximum for . Also we find distance- i spectrum of thorn graphs, , when G is connected - regular graph with diameter 2.

Weak and strong domination in thorn graphs

Let [Formula: see text] be a graph and [Formula: see text] A dominating set [Formula: see text] is a set of vertices such that each vertex of [Formula: see text] is either in [Formula: see text] or has at least one neighbor in [Formula: see text]. The minimum cardinality of such a set is called the domination number of [Formula: see text], [Formula: see text] [Formula: see text] strongly dominates [Formula: see text] and [Formula: see text] weakly dominates [Formula: see text] if (i) [Formula: see text] and (ii) [Formula: see text] A set [Formula: see text] is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of [Formula: see text] if every vertex in [Formula: see text] is strongly (weakly) dominated by at least one vertex in [Formula: see text]. The strong (weak) domination number [Formula: see text] of [Formula: see text] is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs.