A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introductio...
An edge-colored graph is properly connected if for every pair of vertices u and v there exists a pro...
This note introduces the vertex proper connection number of a graph and provides a relationship to t...
Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of...
We say an edge-colored graph is properly connected if, between every pair of vertices, there exists ...
The concept of \emph{proper connection number} of graphs is an extension of proper colouring and is ...
Given a complete graph G, we consider two separate scenarios. First, we consider the minimum number ...
This note introduces the vertex proper connection number of a graph and provides a relationship to t...
AbstractThis note introduces the vertex proper connection number of a graph and provides a relations...
A path in an edge-colored graph is properly colored if no two consecutive edges receive the same col...
AbstractAn edge-colored graph G is k-proper connected if every pair of vertices is connected by k in...
An edge-colored graph G is k-proper connected if every pair of vertices is connected by k internally...
summary:An edge-colored graph $G$ is proper connected if every pair of vertices is connected by a pr...
A properly connected coloring of a given graph G is one that ensures that every two vertices are the...
A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the...
An edge-colored directed graph is called properly connected if, between every pair of vertices, ther...
An edge-colored graph is properly connected if for every pair of vertices u and v there exists a pro...
This note introduces the vertex proper connection number of a graph and provides a relationship to t...
Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of...
We say an edge-colored graph is properly connected if, between every pair of vertices, there exists ...
The concept of \emph{proper connection number} of graphs is an extension of proper colouring and is ...
Given a complete graph G, we consider two separate scenarios. First, we consider the minimum number ...
This note introduces the vertex proper connection number of a graph and provides a relationship to t...
AbstractThis note introduces the vertex proper connection number of a graph and provides a relations...
A path in an edge-colored graph is properly colored if no two consecutive edges receive the same col...
AbstractAn edge-colored graph G is k-proper connected if every pair of vertices is connected by k in...
An edge-colored graph G is k-proper connected if every pair of vertices is connected by k internally...
summary:An edge-colored graph $G$ is proper connected if every pair of vertices is connected by a pr...
A properly connected coloring of a given graph G is one that ensures that every two vertices are the...
A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the...
An edge-colored directed graph is called properly connected if, between every pair of vertices, ther...
An edge-colored graph is properly connected if for every pair of vertices u and v there exists a pro...
This note introduces the vertex proper connection number of a graph and provides a relationship to t...
Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of...