On the edge irregularity strength of corona product of graphs with cycle

Tarawneh, Ibrahim; Hasni, Roslan; Ahmad, Ali; Lau, Gee-Choon; Lee, Sin-Min

doi:10.1142/s1793830920500834

Cited by 13 publications

(13 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Total edge irregularity strength of the graph G , denoted by

is the minimum k for which the graph G has an edge irregular total k -labeling. Some previous results of total edge irregularity strength can be seen in [9] , [10] , [11] .…”

Section: Introductionmentioning

confidence: 74%

The reflexive edge strength on some almost regular graphs

Agustin

Dafik

Utoyo

et al. 2021

Heliyon

View full text Add to dashboard Cite

A function f with domain and range are respectively the edge set of graph G and natural number up to , and a function f with domain and range are respectively the vertex set of graph G and the even natural number up to 2 are called a total k -labeling where 2 . The total k -labeling of graph G by the condition that every two different edges have different weight is called an edge irregular reflexive k -labeling, where for any edge , the weight is . The reflexive edge strength of the graph G , denoted by is the minimum k for graph G which has an edge irregular reflexive k -labelling. In this study, we obtained the of graphs which their vertex degrees show an almost regularity properties.

show abstract

“…Total edge irregularity strength of the graph G , denoted by

is the minimum k for which the graph G has an edge irregular total k -labeling. Some previous results of total edge irregularity strength can be seen in [9] , [10] , [11] .…”

Section: Introductionmentioning

confidence: 74%

The reflexive edge strength on some almost regular graphs

Agustin

Dafik

Utoyo

et al. 2021

Heliyon

View full text Add to dashboard Cite

show abstract

“…Tarawneh et al [14] determined the exact value of edge irregularity strength of corona product of graphs with paths. Tarawneh et al [16] determined the exact value of edge irregularity strength of corona product of graphs with cycle. Recently, Zhang et al [19] determined the exact value of edge irregularity strength of certain families of comb graph.…”

Section: Preliminary Resultsmentioning

confidence: 99%

On edge irregularity strength of line graph and line cut-vertex graph of comb graph

Nagesh¹,

Girish²

2022

NNTDM

View full text Add to dashboard Cite

For a simple graph $G$, a vertex labeling $\phi:V(G) \rightarrow \{1, 2,\ldots,k\}$ is called $k$-labeling. The weight of an edge $xy$ in $G$, written $w_{\phi}(xy)$, is the sum of the labels of end vertices $x$ and $y$, i.e., $w_{\phi}(xy)=\phi(x)+\phi(y)$. A vertex $k$-labeling is defined to be an edge irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, $w_{\phi}(e) \neq w_{\phi}(f)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labeling is called the edge irregularity strength of $G$, written $es(G)$. In this paper, we find the exact value of edge irregularity strength of line graph of comb graph $P_n \bigodot K_1$ for $n=2,3,4$; and determine the bounds for $n \geq 5$. Also, the edge irregularity strength of line cut-vertex graph of $P_n \bigodot K_1$ for $n=2$; and determine the bounds for $n \geq 3$.

show abstract

“…In this paper, we discussed the edge irregularity strength es, as a modification of the well-known irregularity strength, total edge irregularity strength and total vertex irregularity strength (see [19][20][21][22][23][24][25]). We obtained the precise values for edge irregularity strength of triangular grid graph L m n , zigzag graph Z m n and Cartesian product P n □P m □P 2 .…”

Section: Discussionmentioning

confidence: 99%

“…Mushayt [20] determined the edge irregularity strength of Cartesian product of star, cycle with path P 2 and strong product of path P n with P 2 . Tarawneh et al [21][22][23] investigated the exact value of edge irregularity strength of corona product of graph with paths and cycles; and corona product of cycle with isolated vertices, respectively. Ahmad [24] determined the exact value of the edge irregularity strength of corona graph C n ⊙ K 1 (or sun graph S n ).…”

Section: Introductionmentioning

confidence: 99%

On the edge irregularity strength of grid graphs

Tarawneh

Hasni

Ahmad

2020

AKCE International Journal of Graphs and Combinatorics

Self Cite

View full text Add to dashboard Cite

For a simple graph G, a vertex labeling φ : V (G) → {1, 2, . . . , k} is called a vertex k-labeling. For any edge x y in G, its weight w φ (x y) = φ(x) + φ(y). If all the edge weights are distinct, then φ is called an edge irregular k-labeling of G. The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G).In this paper, we determine an exact value of edge irregularity strength for triangular grid graph L m n , zigzag graph Z m n and Cartesian product P n □P m □P 2 .

show abstract

On the edge irregularity strength of corona product of graphs with cycle

Cited by 13 publications

References 16 publications

The reflexive edge strength on some almost regular graphs

The reflexive edge strength on some almost regular graphs

On edge irregularity strength of line graph and line cut-vertex graph of comb graph

On the edge irregularity strength of grid graphs

Contact Info

Product

Resources

About