On Total Irregularity Strength of Double-Star and Related Graphs

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• 作者：Diari Indriati^a ; ^b ; ^{diari_indri@yahoo.co.id" class="auth_mail" title="E-mail the corresponding author} ; Widodo^a ; ^{widodo_mathugm@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Indah Emilia Wijayanti^a ; Kiki Ariyanti Sugeng^c
• 关键词：Totally irregular total k-labeling ; total irregularity strength ; weight ; double-star ; caterpillar
• 刊名：Procedia Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：74
• 期：Complete
• 页码：118-123
• 全文大小：176 K

文摘

Let G = (V, E) be a simple and undirected graph with a vertex set V and an edge set E. A totally irregular total k-labeling f : V ∪ E → {1, 2,. . ., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x1, their weights and are distinct, and for any two different edges xy and x1y1 their weights f (x) + f (xy) + f (y) and f (x1) + f (x1y1) + f (y1) are also distinct. A total irregularity strength of graph G, denoted byts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for double-star S n,m, n, m ≥ 3 and graph related to it, that is a caterpillar S n,2,n, n ≥ 3. The results are and ts(S n,2,n) = n.