TY - JOUR
T1 - On the total irregularity strength of convex polytope graphs
AU - Ahtsham, Syed
AU - Imran, Muhammad
AU - Ali, Usman
N1 - Funding Information:
This research is supported by the Start Up Research Grant 2016 of United Arab Emirates University (Grant No. G00002233)
Publisher Copyright:
© 2021. All Rights Reserved.
PY - 2021
Y1 - 2021
N2 - A vertex (edge) irregular total k-labeling ϕ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2,…, k} in such a way that any two different vertices (edges) have distinct weights. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x, whereas the weight of an edge is the sum of label of the edge and the vertices incident to that edge. The minimum k for which the graph G has a vertex (edge) irregular total k-labeling is called the total vertex (edge) irregularity strength of G. In this paper, we are dealing with infinite classes of convex polytopes generated by prism graph and antiprism graph. We have determined the exact value of their total vertex irregularity strength and total edge irregularity strength.
AB - A vertex (edge) irregular total k-labeling ϕ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2,…, k} in such a way that any two different vertices (edges) have distinct weights. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x, whereas the weight of an edge is the sum of label of the edge and the vertices incident to that edge. The minimum k for which the graph G has a vertex (edge) irregular total k-labeling is called the total vertex (edge) irregularity strength of G. In this paper, we are dealing with infinite classes of convex polytopes generated by prism graph and antiprism graph. We have determined the exact value of their total vertex irregularity strength and total edge irregularity strength.
KW - Irregular assignment
KW - convex polytopes
KW - irregularity strength
KW - vertex irregular total k-labeling
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U2 - 10.22199/issn.0717-6279-3959
DO - 10.22199/issn.0717-6279-3959
M3 - Article
AN - SCOPUS:85117417143
SN - 0716-0917
VL - 40
SP - 1267
EP - 1277
JO - Proyecciones
JF - Proyecciones
IS - 5
ER -