Edge irregular reflexive labeling on sun graph and corona of cycle and null graph with two vertices

Abstract

<p>Let <em>G</em>(<em>V</em>,<em>E</em>) be a simple and connected graph which set of vertices is <em>V</em> and set of edges is <em>E</em>. Irregular reflexive <em>k</em>-labeling f on <em>G</em>(<em>V</em>,<em>E</em>) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,<em>k</em><sub>e</sub>} assignment to edges of graph and the even positive integer {0,2,4,...,2<em>k</em><sub>v</sub>} assignment to vertices of graph. Then, we called as edge irregular reflexive <em>k</em>-labelling if every edges has different weight with <em>k</em> = max{<em>k</em><sub>e</sub>,2<em>k</em><sub>v</sub>}. Besides that, there is definition of reflexive edge strength of <em>G</em>(<em>V</em>,<em>E</em>) denoted as <em>res</em>(<em>G</em>), that is a minimum <em>k</em> that using for labeling <em>f</em> on <em>G</em>(<em>V</em>,<em>E</em>). This paper will discuss about edge irregular reflexive <em>k</em>-labeling for sun graph and corona of cycle and null graph, denoted by <em>C</em><sub>n</sub> ⨀ <em>N</em><sub>2</sub> and make sure about their reflexive edge strengths.</p>