Browsing by Author "Perera, A.A.I."

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Open Access
𝒌 – Graceful Labeling of Triangular Type Grid Graphs 𝑫𝒏(𝑷𝒎) and 𝑳 – Vertex Union of 𝑫𝒏(𝑷𝒎)
(Sri Lanka Institute of Information Technology, 2023-03-25) Indunil, W.K.M.; Perera, A.A.I.
Graph labeling is one of the most popular research topics in the field of graph theory. Prime labeling, antimagic labeling, radio labeling, graceful labeling, lucky labeling, and incidence labeling are some of the labeling techniques. Among the above-mentioned techniques, graceful labeling is one of the most engaging graph labeling techniques with a vast amount of real-world applications. Over the past few decades, plenty of studies have been conducted on this area in various dimensions. Grid graphs are very much useful in applications of circuit theory, communication networks, and transportation networks. However, in the literature, there are not many research papers on the graceful labeling of grid graphs except a few on odd graceful labeling. In our work, we prove that triangular-type grid graphs, 𝐷𝑛(𝑃𝑚) and 𝐿 – vertex union of 𝐷𝑛(𝑃𝑚) admit 𝑘 – general graceful labeling and 𝑘 – even and 𝑘 – odd graceful labeling. Further, we introduce combinatorial proofs for them as well.
Open Access
Odd Prime Labeling of Snake Graphs
(Sri Lanka Institute of Information Technology, 2023-03-25) De Silva, K.H.C.; Perera, A.A.I.
Graph theory is one of the branches of mathematics which is concerned with the networks of points connected by lines. One of the most important research areas in graph theory is graph labeling, which dates back to the 1960s. Graph labeling is assigning integers to the vertices, edges, or both depending on conditions. Labeled graphs are helpful in mathematical models for a wide range of applications such as in coding theory, circuit theory, computer networks, and in cryptography as well. There are various types of graph labeling techniques in graph theory such as radio labeling, graceful labeling, prime labeling, antimagic labeling, and lucky labeling, etc. In this research, we use one of the variations of prime labeling called odd prime labeling of snake graphs. Recent works on odd prime labeling investigate about families of snake graphs, complete graphs, etc and there they discuss about one odd integer sequence only. In this research, we introduce odd prime labeling method for snake graphs for any odd integer sequence and we give a proof for it as well.