📄 Abstract
In this paper proper d-lucky number is computed for slim tree and Christmas tree. Proper d-lucky number is defined as For a vertex u in a graph G, let N(u)={v∈V(G)/uv∈E(G). Let l∶V(G)→{1,2,…,k} be a labeling of vertices of a graph G by positive integers. Define c(u)= ∑_(v∈N(u))▒〖l(v)+ d(u)〗, where d(u) denotes the degree of u. Define a labeling l as d-lucky if c(u)≠c(v), for every pair of adjacent vertices u and v in G. The d-lucky number of a graph G, denoted by ɳ_dl (G), is the least positive k such that G has a d-lucky labeling with {1,2,…,k} as the set of labels. A d-lucky labeling is said to be proper d-lucky labeling if for every pair of adjacent vertices u and v in G, u≠v, and is denoted by ƞ_pdl (G).
🏷️ Keywords
📚 How to Cite:
Chiranjilal kujur , PROPER d-LUCKY LABELING FOR SOME FAMILY OF TREE GRAPHS , Volume 12 , Issue 6, June 2026, EPRA International Journal of Multidisciplinary Research (IJMR) , Pages: 401 - 405 ,