Advanced Materials Science Research

Graph Theory-peer-review-journals

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically; see Graph (discrete mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics. Graph In one restricted but very common sense of the term,[1][2] a graph is an ordered pair G = (V, E) comprising: V a set of vertices (also called nodes or points); E ⊆ {{x, y} | (x, y) ∈ V2 ∧ x ≠ y} a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with two distinct vertices). undirected simple graph. In the edge {x, y}, the vertices x and y are called the endpoints of the edge. The edge is said to join x and y and to be incident on x and on y. A vertex may exist in a graph and not belong to an edge. Multiple edges are two or more edges that join the same two vertices. In one more general sense of the term allowing multiple edges,[3][4] a graph is an ordered triple G = (V, E, Ï•) comprising: V a set of vertices (also called nodes or points); E a set of edges (also called links or lines);  

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