On certain topological indices of the derived graphs of subdivision graphs

The derived graph [G]† of a graph G is the graph having the same vertex set as G, with two vertices of [G]† being adjacent if and only if their distance in G is two. Topological indices are valuable in the study of QSAR/QSPR. There are numerous applications of graph theory in the field of structural chemistry. In this paper, we compute generalized Randi´c, general Zagreb, general sum-connectivity, ABC, GA, ABC4, and GA5 indices of the derived graphs of subdivision graphs.Publisher's Versio

Connected cototal domination number of a graph

A dominating set $D subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $langle D rangle$ is connected and $langle V-D rangle neq phi$, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of $D$ is connected cototal dominating set. The connected cototal domination number $gamma_{ccl}(G)$ of $G$ is the minimum cardinality of a minimal connected cototal dominating set of $G$. In this paper, we begin an investigation of connected cototal domination number and obtain some interesting results

QSPR Analysis of certain Distance Based Topological Indices

In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we study the QSPR analysis of selected distance and degree-distance based topological indices. Our study reveals some important results which help us to characterize the useful topological indices based on their predicting power

Semientire Domination in Graphs

ABSTRACT The vertices and edges of a graph G are called the elements of G. We say that a vertex v dominates an edge e if e ∈‫ܰۃ‬ሾ‫ݒ‬ሿ‫.ۄ‬A set D ⊆ V of G = (V, E) is said to be a semientire dominating set if every vertex in V − D is adjacent to at least one vertex in D and every edge in G is dominated by some vertex in D. The semientire domination number ε s (G) of G is the minimum cardinality taken over all the minimal semientire dominating sets of G. In this paper, exact values of ε s (G)for some standard graphs are obtained. Further, bounds on ε s (G)and Nordhaus-Gaddum type results are established