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Strong sum distance in fuzzy graphs.

Mini Tom¹, Muraleedharan Shetty Sunitha²

¹Department of Mathematics, SCMS School Of Engineering and Technology, Karukutty, 683 582 Kerala India.

|July 18, 2015

Summary

This study introduces strong sum distance, a metric for fuzzy graphs. It analyzes graph properties like eccentricity and centers, revealing insights into fuzzy trees and self-centered fuzzy graphs.

Keywords:

Boundary Fuzzy cycle Fuzzy graph Fuzzy tree Interior Strong sum distance

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Area of Science:

Graph Theory
Fuzzy Mathematics
Metric Spaces

Background:

Fuzzy graphs are extensions of graph theory incorporating uncertainty.
Existing distance metrics in fuzzy graphs have limitations.
Understanding graph centrality and structure is crucial in various applications.

Purpose of the Study:

Introduce and define the strong sum distance metric for fuzzy graphs.
Investigate fundamental graph properties using this new metric.
Characterize specific types of fuzzy graphs, such as self-centered and complete fuzzy graphs.

Main Methods:

Definition of strong sum distance as a metric on fuzzy graphs.
Application of the metric to derive concepts of eccentricity, radius, diameter, and center.
Analysis of properties related to eccentric, peripheral, central, boundary, and interior nodes.
Characterization of self-centered complete fuzzy graphs and fuzzy cycles.

Main Results:

Established properties of eccentric, peripheral, and central nodes in fuzzy graphs.
Characterized self-centered complete fuzzy graphs and identified conditions for self-centered fuzzy cycles.
Proved that eccentric nodes in fuzzy trees are end nodes, and identified conditions for nodes to be eccentric or peripheral.
Determined that the center of a fuzzy tree comprises one or two adjacent nodes.
Introduced and studied properties of boundary and interior nodes based on the strong sum distance.

Conclusions:

The strong sum distance provides a novel framework for analyzing fuzzy graph structures.
The metric yields significant results regarding the centrality and peripheral nature of nodes in fuzzy trees.
The study contributes to a deeper understanding of fuzzy graph properties and their characterizations.