A Study on Graph Theory of Path Graphs

In a simple graph the G is define as G = (V, E), here V is known as non-empty set of vertices and E is consider as edges. It is the set of unordered combination of unique elements of V. A simple graph has their points of confinement in demonstrating this present reality. Rather, we use multigraphs, which comprise of vertices and undirected edges between these vertices, with various edges between sets of vertices permitted. In this field of diagram hypothesis, a path graph or straight diagram is a graph whose vertices can be recorded in the request to such an extent that the edges are the place I = 1, 2, … , n ? 1. Proportionally, a way with in any event two vertices is associated and has two terminal (vertices that have degree 1), while all others (assuming any) have degree 2. The path graph of a diagram G is acquired by depicting the path in G by vertices and joining two vertices when the comparing path in G structure a path or a cycle The path graph of a graph G is obtained by describing the paths in G by vertices and joining two vertices when the corresponding paths in G form a path or a cycl

Independence Number in Path Graphs

In the paper we present results, which allow us to compute the independence numbers of $P_2$-path graphs and $P_3$-path graphs of special graphs. As $P_2(G)$ and $P_3(G)$ are subgraphs of iterated line graphs $L^2(G)$ and $L^3(G)$, respectively, we compare our results with the independence numbers of corresponding iterated line graphs

The reversing number of a diagraph

AbstractA minimum reversing set of a diagraph is a smallest sized set of arcs which when reversed makes the diagraph acyclic. We investigate a related issue: Given an acyclic diagraph D, what is the size of a smallest tournament T which has the arc set of D as a minimun reversing set? We show that such a T always exists and define the reversing number of an acyclic diagraph to be the number of vertices in T minus the number of vertices in D. We also derive bounds and exact values of the reversing number for certain classes of acyclic diagraphs