Graphs are used for modelling multiple relations and processes in computer, engineering, physical, and biological sciences. Moreover, they are also used in information systems, social sciences, and many other branches of basic and applied sciences

Researchers model their problems by using graph structure in different fields of sciences. The term network is used for a graph in which attributes are associated with the vertices and edges of the graph. The application of distance in graphs can be found in image processing, optimization, networking, pattern recognition, and navigation. Graph is an ordered triple G=(V,E,ψ), where the vertex set V is non-empty; the edge set E may be empty and ψ is the function from the edge set to V×V. If ψ(e)=(v,v) then e is called a loop, otherwise it is called a simple edge. The minimum number of edges between two vertices u and v is called the distance between these vertices and denoted by d(u,v).

The aim of this Special Issue is to bring together original research and review articles that discuss distances in graphs. We welcome submissions from researchers in the field, especially experts in graph theory. We hope that this Special Issue reinforces the phenomenon of distance in graphs to unify the terminology used in this subject area. Submissions discussing metric dimensions, metric chromaticity, different graph indices, and fixed-point theorem are particularly encouraged.

Potential topics include but are not limited to:

Potential topics include but are not limited to the following:

• • Metric dimensions in graph theory
• • Least and maximum eigenvalues of the graph via adjacency distance and 1-2 adjacency matrices of graphs
• • Image segmentation via graph cut
• • Graph indices in graph theory
• • Fixed point theory and its application in graphs
• • Domination and total domination number in graphs, Hamiltonian and Eulerian Problems in graphs