On Super Mean Labeling for Total Graph of Path and Cycle

Inayah, Nur; Sudarsana, I Wayan; Musdalifah, Selvy; Mangesa, Nurhasanah Daeng

doi:10.1155/2018/9250424

Cited by 3 publications

(2 citation statements)

References 2 publications

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“…The total graph of path T (P n ), studied in [16], for super mean labeling. The total graph of path T (P 5 ) is shown in the Figure 2.…”

Section: B Total Graph Of Path T (Pn )mentioning

confidence: 99%

On Mixed Metric Dimension of Some Path Related Graphs

Raza

2020

IEEE Access

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A vertex k ∈ V G determined two elements (vertices or edges) , m ∈ V G ∪ E G , if d G (k,) = d G (k, m). A set R m of vertices in a graph G is a mixed metric generator for G, if two distinct elements (vertices or edges) are determined by some vertex set of R m. The least number of elements in the vertex set of R m is known as mixed metric dimension, and denoted as dim m (G). In this paper, the mixed metric dimension of some path related graphs is obtained. Those path related graphs are P 2 n the square of a path, T (P n) total graph of a path, the middle graph of a path M (P n), and splitting graph of a path S(P n). We proved that these families of graphs have constant and unbounded mixed metric dimension, respectively. We further presented an improved result for the metric dimension of the splitting graph of a path S(P n). INDEX TERMS Mixed metric dimension, Metric dimension, Edge metric dimension, Path related graphs.

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“…The total graph of path T (P n ), studied in [16], for super mean labeling. The total graph of path T (P 5 ) is shown in the Figure 2.…”

Section: B Total Graph Of Path T (Pn )mentioning

confidence: 99%

On Mixed Metric Dimension of Some Path Related Graphs

Raza

2020

IEEE Access

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“…e classical meanness property of some graphs based on line graphs was considered in [5]. For some recent applications of the total graphs, see, e.g., [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Omega Index of Line and Total Graphs

Demırcı

Çevik

et al. 2021

Journal of Mathematics

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A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.

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An application of super mean and magic graphs labeling on cryptography system

Sudarsana

Suryanto

Lusianti

et al. 2021

J. Phys.: Conf. Ser.

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An edge-magic total (EMT) labeling on a simple graph G with p vertices and q edges is a bijection f: V∪E→{1, 2, …, p + q} such that for each edge xy of G, f(x) + f(xy) + f(y) = k, for a fixed positive integer k. Moreover, an EMT labeling f is a super edge-magic total labeling (SEMT) if f(V) = {1, 2, …, p}. Furthermore, a graph G is called a super mean (SM) graph if there exists an injective function f from the vertices of G to {0,1,2,…,q} such that when each edge uv is labeled with (f(u) +f(v))/2 when f(u) +f(v) is even, and (f(u) +f(v) + 1)/2 when f(u) +f(v) is odd, then the resulting edge labels are distinct. There are two essentials results that will be proposed in this paper. In the first result, we show that a graph (n, 1) − F Caterpillar has a SM labeling and a graph Hu,y K ¯ n has a SEMT labeling. In the second result, we will give an application of these labeling to increase the security level of Affine Cipher in which to encrypt a text on socials media.

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On Super Mean Labeling for Total Graph of Path and Cycle

Cited by 3 publications

References 2 publications

On Mixed Metric Dimension of Some Path Related Graphs

On Mixed Metric Dimension of Some Path Related Graphs

Omega Index of Line and Total Graphs

An application of super mean and magic graphs labeling on cryptography system

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