Vertex irregular reflexive labeling of prisms and wheels. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Tanna, Dushyant; Ryan, Joe; Semaničová-Feňovčíková, Andrea; Bača, Martin
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 17:Issue 1(2020)
• Page Start: 51
• Page End: 59
• Publication Date: 2020-01-02
• Subjects: Vertex irregular reflexive labeling -- Reflexive vertex strength -- Prism -- Wheel -- Fan graph
• DOI: 10.1016/j.akcej.2018.08.004
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: For a graph G we define k -labeling ρ such that the edges of G are labeled with integers { 1, 2, …, k e } and the vertices of G are labeled with even integers { 0, 2, …, 2 k v }, where k = max { k e, 2 k v } . The labeling ρ is called a vertex irregular reflexive k -labeling if distinct vertices have distinct weights, where the vertex weight is defined as the sum of the label of that vertex and the labels of all edges incident this vertex. The smallest k for which such labeling exists is called the reflexive vertex strength of G . In this paper, we give exact values of reflexive vertex strength for prisms, wheels, fan graphs and baskets.