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Irregularity strength of triangular snake and double triangular snake. (English) Zbl 1251.05069

Summary: If positive weights are assigned to the edges of a graph \(G\), then degree of a vertex is the sum of the weights of edges that are incident to the vertex. A graph with weighted edges is said to be irregular if the degrees of the vertices are distinct. The irregularity strength of a graph is the smallest number \(s\) such that the edges can be weighted with {\(1,2,3,\dots,s\)} and be irregular. This notion was defined in [G. Chartrand, M. S. Jacobson, J. Lehel, O. R. Ollermann, S. Ruiz and F. Saba, “Irregular networks,” Congr. Numerantium 64, 197–210 (1988; Zbl 0671.05060)]. In this paper, we determine the irregularity strength of triangular and double triangular snakes.

MSC:

05C22 Signed and weighted graphs

Citations:

Zbl 0671.05060
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