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Local Inclusive Distance Vertex Irregular Graphs

by Kiki Ariyanti Sugeng, Denny Riama Silaban, Martin Bača and Andrea Semaničová-Feňovčíková

Mathematics 2021, 9(14), 1673; https://doi.org/10.3390/math9141673 - 16 Jul 2021

Cited by 2 | Viewed by 2639

Let

G = (V, E)

be a simple graph. A vertex labeling

f : V (G) \to {1, 2, \dots, k}

is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex [...] Read more.

Let

G = (V, E)

be a simple graph. A vertex labeling

f : V (G) \to {1, 2, \dots, k}

is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices

x, y \in V (G)

their weights are distinct, where the weight of a vertex

x \in V (G)

is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for

d = 1

and determine the precise values of the corresponding graph invariant for certain families of graphs. Full article

(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory)

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