Lucky and Proper Lucky Labeling of Quadrilateral Snake Graphs

Abstract

Abstract The labeling is said to be lucky labeling of the graph if the vertices of the graph are labeled by natural number with satisfying the condition that sum of labels over the adjacent of the vertices in the graph are not equal and if vertices are isolated vertex then the sum of the vertex is zero. The least natural number which labelled the graph is the lucky number. The Lucky Number of graph G is denoted by η(G). The labeling defined as proper labeling if the vertices of the graph are labeled by natural number with fulfilling the condition that label of adjacent vertices is not the same. The labeling is defined as proper lucky labeling if labeling is proper and also lucky. The proper lucky number of graph G is denoted by η p (G). Here we obtain a lucky number and proper lucky number for family of quadrilateral snake graph such as quadrilateral snake graph, double quadrilateral snake graph, alternate quadrilateral snake graph and double alternate quadrilateral snake graph.