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An edge irregular total [Formula: see text]-labeling on simple and undirected graph [Formula: see text] is a map [Formula: see text] such that for any different edge [Formula: see text] and [Formula: see text] their weights [Formula: see text] and [Formula: see text] are distinct. The minimum [Formula: see text] for which the graph [Formula: see text] has an edge irregular total [Formula: see text]-labeling is called the total edge irregularity strength of [Formula: see text] and is denoted by tes[Formula: see text]. In this paper, we determine the exact value of the total edge irregularity strength of families of ladder-related graphs, namely triangular ladder graphs, diagonal ladder graphs and circular triangular ladder graphs.

Oral antidiabetic drugs mostly give unwanted side effects, so it is necessary to develop a traditional treatment system for diabetes mellitus which is relatively safe. The purpose of this study was to determine the effect of single clove garlic on decreasing blood sugar levels, decreasing malondialdehyde levels, increasing insulin levels, and decreasing insulin resistance in experimental rats induced by streptozotocin 50 mg / KgBB. (P1) therapy of single clove garlic 50 mg/kgBB, (P2) therapy of single clove of garlic 75 mg/KgBB, (P3) therapy of single clove of garlic 125 mg/KgBB. The most effective dose in this study was 125 mg/KgBB. Comparison test the mean of each group with the Manova test. The flavonoids in single clove garlic have been shown to be powerful agents to reduce the pathogenesis of diabetes and its complications.

For any simple undirected graph G(V, E), a map f : V ⋃ E → {1, 2, …, k} such that for any different edges xy and x’y’ their weights are distinct is called an edge irregular total k-labeling. The weight of edge xy is defined as the sum of edge label of xy, vertex label of x and vertex label of y. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G and is denoted by tes(G). In this paper, we determine the exact value of the total edge irregularity strength of odd arithmetic book graph Bn (C 3, 5, 7, …2n+1) and even arithmetic book graph Bn (C 4, 6, 8, …, 2n+2) of n sheets. We found that the tes of odd arithmetic book graph Bn (C 3, 5, 7, …, 2n+1) of n sheets is equal to the ceiling function of n 2 + n + 3 3 and the tes of even arithmetic book graph Bn (C 4, 6, 8, …, 2n+2) is equal to the ceiling function of n 2 + 2 n + 3 3 .

Let G = (V (G), E(G)) be a connected simple undirected graph with non empty vertex set V (G) and edge set E(G). For a positive integer k, by an edge irregular total k−labeling we mean a function f : V (G) ∪ E(G) → {1, 2, ..., k} such that for each two edges ab and cd, it follows that f (a) + f (ab) + f (b) = f (c) + f (cd) + f (d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k−labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs.