Abstract:
For a simple graph G, a vertex k-labeling ?:V(G)?{1,2,…,k} is termed edge irregular if every edge xy?E(G) satisfies w_? (xy)=?(x)+?(y), and all such weights are distinct. The minimum such k is called the edge irregularity strength of G, denoted es(G). This paper investigates the edge irregularity strength of triangular grid graphs, particularly focusing on the subclass L_2^m, for which we determine the exact value of es(L_2^m). For the general case L_n^m, we propose a labeling strategy and derive a near-optimal upper bound. Furthermore, we establish a tight upper bound for cycle graphs C_n, improving upon existing estimates. A significant contribution is the exact determination of the edge irregularity strength for the rooted product graph C_n°P_2, where each vertex of the cycle is extended by a path of length two. Our results are supported by constructive labeling schemes and rigorous combinatorial arguments, offering new insights into the structural behavior of edge irregular labelings across diverse graph families. Edge irregular labeling is a compelling area of graph theory that explores vertex assignments yielding distinct edgeweights.
Page(s):
174-174
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
cycle graph
,
edge irregularity strength
,
rooted product graph
,
triangular grid graph
,
Edge irregular labeling