On H-irregularity strengths of G-amalgamation of graphs

Ashraf, Faraha; Bača, Martin; Semaničová-Feňovčíková, Andrea; Shabbir, Ayesha

doi:10.5614/ejgta.2017.5.2.13

Cited by 3 publications

(2 citation statements)

References 18 publications

(23 reference statements)

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“…The precise value of the total H-irregularity strength of G-amalgamation of graphs is given in [8] and it proves that the lower bound in Theorem 1.1 is tight.…”

Section: Introductionmentioning

confidence: 86%

On cycle-irregularity strength of ladders and fan graphs

Ashraf

Bača

Semaničová-Feňovčíková

et al. 2020

ejgta

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“…The precise value of the total H-irregularity strength of G-amalgamation of graphs is given in [8] and it proves that the lower bound in Theorem 1.1 is tight.…”

Section: Introductionmentioning

confidence: 86%

On cycle-irregularity strength of ladders and fan graphs

Ashraf

Bača

Semaničová-Feňovčíková

et al. 2020

ejgta

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“…Ashraf F. et al [3] found the total P m -irregularity strength of P n with m, n both integer, 2 ≤ m ≤ n, the total C m -irregularity strength of ladder graph L n with n ≥ 3 and m = 4 or m = 6, and the total C 3 -irregularity strength of fan graph F n . Ashraf F. et al [4] determined the exact value of total H-irregularity strengths of G-amalgamation of graphs. Agustin et al [5] found the total H-irregularity strength of shackle and vertex amalgamation of G, namely ths(Shack(H, v, n)), ths(c(Shack(H, v, n))), ths(Amal(H, v, n)) and ths(c(Amal(H, v, n))).…”

Section: Introductionmentioning

confidence: 99%

Computing the Total $H$-irregularity Strength of Edge Comb Product of Graphs

Wahyujati¹,

Susanti²

2022

Preprint

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A simple undirected graph $\Gamma=(V_\Gamma,E_\Gamma)$ admits an $H$-covering if every edge in $E_\Gamma$ belongs to at least one subgraph of $\Gamma$ that isomorphic to a graph $H$. For any graph $\Gamma$ admitting $H$-covering, a total Labelling $\beta: V_\Gamma \cup E_\Gamma \longrightarrow \{1,2,\dots,p\}$ is called an $H$-irregular total $p$-labelling of $\Gamma$ if every two different subgraphs $H_1$ and $H_2$ of $\Gamma$ isomorphic to $H$ have distinct weights where the weight $w_\beta(K)$ of subgraph $K$ of $\Gamma$ is defined as $w_f(K):=\displaystyle \sum_{v\in V_K} f(v) + \sum_{e\in E_K} f(e)$. The smallest number $p$ for which a graph $\Gamma$ admits an $H$-irregular total $p$-labelling is called the total $H$-irregularity strength of $\Gamma$ and is denoted by $ths(\Gamma)$. In this paper, we determine the total $H$-irregularity strength of edge comb product of two graphs.

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On H-irregularity strength of cycles and diamond graphs

Labane

Bouchemakh

Semaničová-Feňovčíková

2021

Discrete Math. Algorithm. Appl.

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A simple graph [Formula: see text] admits an [Formula: see text]-covering if every edge in [Formula: see text] belongs to at least one subgraph of [Formula: see text] isomorphic to a given graph [Formula: see text]. The graph [Formula: see text] admits an [Formula: see text]-irregular total[Formula: see text]-labeling [Formula: see text] if [Formula: see text] admits an [Formula: see text]-covering and for every two different subgraphs [Formula: see text] and [Formula: see text] isomorphic to [Formula: see text], there is [Formula: see text], where [Formula: see text] is the associated [Formula: see text]-weight. The total[Formula: see text]-irregularity strength of [Formula: see text] is [Formula: see text]. In this paper, we give the exact values of [Formula: see text], where [Formula: see text]. For the versions edge and vertex [Formula: see text]-irregularity strength [Formula: see text] and [Formula: see text], respectively, we determine the exact values of [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is the diamond graph.

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On H-irregularity strengths of G-amalgamation of graphs

Abstract: A simple graph G =

Cited by 3 publications

References 18 publications

On cycle-irregularity strength of ladders and fan graphs

On cycle-irregularity strength of ladders and fan graphs

Computing the Total $H$-irregularity Strength of Edge Comb Product of Graphs

On H-irregularity strength of cycles and diamond graphs

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