On additive vertex labelings

Indonesian Journal of Combinatorics

卷:4

Christian Barrientos¹ 

[1] Valencia College;

关键词: additive vertex labeling;    harmonious;    corona product;    unicyclic;    polyiamonds;   

DOI  :  10.19184/ijc.2020.4.1.5

来源: DOAJ

【 摘 要 】

In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with n edges and at most n vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all n-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle C₃ in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle C_4t to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.

【 授权许可】

Unknown