On the Distinguishing Number of Functigraphs

Fazil, Muhammad; Murtaza, Muhammad; Ullah, Zafar; Ali, Usman; Javaid, Imran

doi:10.3390/sym10080332

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Real systems of contrasting nature can be visualized through functigraph structure that consists of two copies of the identical network. The authors' work in [16] similar to this paper work but on a different platform along with the articles in [17] have really served as a motivational factor.…”

Section: Motivational Factormentioning

confidence: 78%

On Coloring Catalan Number Distance Graphs and Interference Graphs

Yegnanarayanan

Yegnanarayanan²,

Bălaş

2018

Symmetry

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A vertex coloring of a graph G is a mapping that allots colors to the vertices of G. Such a coloring is said to be a proper vertex coloring if two vertices joined by an edge receive different colors. The chromatic number χ ( G ) is the least number of colors used in a proper vertex coloring. In this paper, we compute the χ of certain distance graphs whose distance set elements are (a) a finite set of Catalan numbers, (b) a finite set of generalized Catalan numbers, (c) a finite set of Hankel transform of a transformed sequence of Catalan numbers. Then while discussing the importance of minimizing interference in wireless networks, we probe how a vertex coloring problem is related to minimizing vertex collisions and signal clashes of the associated interference graph. Then when investigating the χ of certain G ( V , D ) and graphs with interference, we also compute certain lower and upper bound for χ of any given simple graph in terms of the average degree and Laplacian operator. Besides obtaining some interesting results we also raised some open problems.

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Section: Motivational Factormentioning

confidence: 78%

On Coloring Catalan Number Distance Graphs and Interference Graphs

Yegnanarayanan

Yegnanarayanan²,

Bălaş

2018

Symmetry

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“…Kang et al [18] investigated the zero forcing number of functigraphs on complete graphs, on cycles, and on paths. Fazil et al [13,14] have studied fixing number and distinguishing number of functigraphs. The aim of this paper is to study the variation of location-domination number in passing from a graph to its functigraph and to find its sharp lower and upper bounds.…”

Section: Introductionmentioning

confidence: 99%

Locating-dominating sets of functigraphs

Murtaza

Fazil

Javaid

2019

Theoretical Computer Science

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A locating-dominating set of a graph G is a dominating set of G such that every vertex of G outside the dominating set is uniquely identified by its neighborhood within the dominating set. The location-domination number of G is the minimum cardinality of a locating-dominating set in G. Let G 1 and G 2 be the disjoint copies of a graph G and f :In this paper, we study the variation of the location-domination number in passing from G to F f G and find its sharp lower and upper bounds. We also study the location-domination number of functigraphs of the complete graphs for all possible definitions of the function f . We also obtain the location-domination number of functigraph of a family of spanning subgraph of the complete graphs.

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“…[12] Let W 1 , W 2 , ..., W t are disjoint twin sets of connected graph G and m = max{|W i | : where 1 ≤ i ≤ t}, then Dist(G) ≥ m.…”

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confidence: 99%

Distinguishing Number of Non-Zero Component Graphs

Javaid,

Murtaza,

Benish

2019

Preprint

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A non-zero component graph G(V) associated to a finite vector space V is a graph whose vertices are non-zero vectors of V and two vertices are adjacent, if their corresponding vectors have at least one non-zero component common in their linear combination of basis vectors. In this paper, we extend the study of properties of automorphisms of non-zero component graphs. We prove that every permutation of basis vectors can be extended to an automorphism of G(V). We prove that the symmetric group of basis vectors of V is isomorphic to the automorphism group of G(V). We find the distinguishing number of the graph for both of the cases, when the number of field elements of vector space V are 2 or more than 2.

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On the Distinguishing Number of Functigraphs

Cited by 3 publications

References 25 publications

On Coloring Catalan Number Distance Graphs and Interference Graphs

On Coloring Catalan Number Distance Graphs and Interference Graphs

Locating-dominating sets of functigraphs

Distinguishing Number of Non-Zero Component Graphs

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