Directed Neutrosophic Graph using Morphological Operators  and Its Applications

Abraham Jacob; Ramkumar P. B.; Dhanya P. M.

Authors

Abraham Jacob Research Scholar, Department of Mathematics, Rajagiri School of Engineering & Technology, affiliated to APJ Abdul Kalam Technological University;
Ramkumar P. B. Professor, Department of Mathematics, Rajagiri School of Engineering & Technology; .
Dhanya P. M. Professor, Department of Computer Science and Business Systems, Rajagiri School of Engineering & Technology;

Keywords:

Connected directed graphs, Morphological dilation, erosion, M induced edge and vertex sequence. Neutrosophic directed graph, Directed Neutrosophic Graph Morphological Network (DNG-MN).

Abstract

Connectedness provides well suited solutions for several application problems. In Graph theory,
graph is connected when there exist a path between any two arbitrary vertices. Neutrosophic set theory to
gether with Morphological operators are useful for constructing the Neutrosophic directed connected subgraphs
(NDCS).Using NDCS, method to generate an ordering of subgraphs and construction of spanning trees is pre
sented in this paper. M induced vertex sequences and M induced Edge sequences are defined. These sequences
generate spanning tree filtration of the graph. Algorithms are given for obtaining such filtrations. Directed
Neutrosophic Morphological Network (DNG-MN) is defined. The spanness of a Neutrosophic graph induced
by Morphological dilation is given in the paper. Some applications of these concepts are also discussed in this
paper.

DOI: 10.5281/zenodo.17096007