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 -