Select the correct alternative from the given choices. Which...

Select the correct alternative from the given choices. Which of the following statements are true? (i) Any graph which contains some parallel edges is called a multigraph. (ii) An edge of a graph which joins a node to itself is called a self-loop. (iii) If there is no more than one edge between a pair of nodes, then such a graph is called simple-graph. (iv) In a digraph, every edge is directed with an ordered pair. (A) Only (i), (ii) and (iv) are correct (B) Only (iii) and (iv) are correct (C) Only (i) and (iii) are correct (D) All are correct

Select the correct alternative from the given choices.
Which of the following statements are true?
(i) Any graph which contains some parallel edges is called a multigraph.
(ii) An edge of a graph which joins a node to itself is called a self-loop.
(iii) If there is no more than one edge between a pair of nodes, then such a graph is called simple-graph.
(iv) In a digraph, every edge is directed with an ordered pair.
(A) Only (i), (ii) and (iv) are correct
(B) Only (iii) and (iv) are correct
(C) Only (i) and (iii) are correct
(D) All are correct

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Key Concepts

Simple Graph

A simple graph is a graph that does not allow multiple edges between the same pair of vertices or self-loops. This restriction simplifies the structure of the graph and is often used as the standard form in many theoretical discussions and practical applications.

Directed Graph (Digraph)

A directed graph, or digraph, is characterized by edges that have an orientation, meaning each edge is an ordered pair of vertices. This directionality is essential in modeling scenarios where the relationships between entities are not reciprocally identical, such as in networks or flow systems.

Multigraph

A multigraph is a type of graph in which multiple edges between the same pair of vertices are allowed. This means that parallel edges can exist, and the focus is on the possibility of these repeated connections, which differentiates multigraphs from other types of graphs.

Self-loop

A self-loop is an edge that connects a vertex to itself within a graph. This concept is crucial in graph theory as it can affect properties like connectivity and degree, and it distinguishes some graphs from simpler forms where such loops are not allowed.

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