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Strong sum distance in fuzzy graphs.

Tom M, Sunitha MS - Springerplus (2015)

Bottom Line: We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes.The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced.Some properties of boundary nodes, interior nodes and complete nodes are studied.

View Article: PubMed Central - PubMed

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

ABSTRACT
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.

No MeSH data available.


Complete node in a fuzzy graph.
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Fig23: Complete node in a fuzzy graph.

Mentions: In crisp graph a vertex v of G is a boundary vertex of every vertex distinct from v if and only if v is a complete vertex of G (Chartrand and Zang 2006) but in fuzzy graphs, based on strong sum distance a complete node need not be a boundary node as shown in Figure 23. Node u is a complete node but it is not a boundary node. Also it may be noted that a node which is a boundary node of all other nodes need not be complete. Node w is boundary node of all other nodes, but it is not complete.Figure 23


Strong sum distance in fuzzy graphs.

Tom M, Sunitha MS - Springerplus (2015)

Complete node in a fuzzy graph.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4499336&req=5

Fig23: Complete node in a fuzzy graph.
Mentions: In crisp graph a vertex v of G is a boundary vertex of every vertex distinct from v if and only if v is a complete vertex of G (Chartrand and Zang 2006) but in fuzzy graphs, based on strong sum distance a complete node need not be a boundary node as shown in Figure 23. Node u is a complete node but it is not a boundary node. Also it may be noted that a node which is a boundary node of all other nodes need not be complete. Node w is boundary node of all other nodes, but it is not complete.Figure 23

Bottom Line: We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes.The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced.Some properties of boundary nodes, interior nodes and complete nodes are studied.

View Article: PubMed Central - PubMed

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

ABSTRACT
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.

No MeSH data available.