Quotient Labeling of Corona of Ladder Graphs

Sumathi, P.; Rathi, A.; Mahalakshmi, A.

doi:10.29027/ijirase.v1.i3.2017.80-85

Cited by 4 publications

(3 citation statements)

References 2 publications

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“…and V 2 have m and n points, we write G = K m,n . A fan graph [21] F m,n , is defined as the graph join K m + P n , where K m is the empty graph on m vertices and P n is the path graph on n vertices, where [18,22] L n is defined by L n = P n K 2 , where P n is a path with n vertices, denotes the Cartesian product and K 2 is a complete graph with two vertices.…”

Section: Preliminariesmentioning

confidence: 99%

Grundy number of corona product of some graphs

Stella Maragatham,

Subramanian

2023

Proyecciones (Antofagasta)

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The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex u colored with color i, 1 ≤ i ≤ k, is adjacent to i – 1 vertices colored with each color j, 1 ≤ j ≤ i − 1. In this paper we obtain the Grundy number of corona product of some graphs, denoted by G ◦ H. First, we consider the graph G be 2-regular graph and H be a cycle, complete bipartite, ladder graph and fan graph. Also we consider the graph G and H be a complete bipartite graphs, fan graphs.

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Section: Preliminariesmentioning

confidence: 99%

Grundy number of corona product of some graphs

Stella Maragatham,

Subramanian

2023

Proyecciones (Antofagasta)

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“…Sumathi and Rathi introduced the quotient labeling number for a wide family of ladder graphs, namely, closed triangular ladder, open triangular ladder, closed ladder, open ladder, step ladder, slanting ladder, and open diagonal ladder [11]. Baskar, referring to the flooring function edge labels, defined the logarithmic mean labeling on graphs and studied the logarithmic meanness of different ladderrelated graphs [12].…”

Section: Introductionmentioning

confidence: 99%

A Study on C‐Exponential Mean Labeling of Graphs

Baskaran

Ganapathy

2022

Journal of Mathematics

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A function h is mentioned as a C -exponential mean labeling of a graph G V , E that has s vertices and r edges if h : V G ⟶ 1 , 2 , 3 , ⋯ , r + 1 is injective and the generated function h ∗ : E G ⟶ 2 , 3 , 4 , ⋯ , r + 1 defined by h ∗ a b = 1 / e h b h b / h a h a 1 / h b − h a , for all a b ∈ E G , is bijective. A graph which recognizes a C -exponential mean labeling is defined as C -exponential mean graph. In the following study, we have studied the exponential meanness of the path, the graph triangular tree of T n , C m P n , cartesian product of two paths P m ▫ P n , one-sided step graph of S T n , double-sided step graph of 2 S T 2 n , one-sided arrow graph of A r s , double-sided arrow graph of D A r s , and subdivision of ladder graph S L t .

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“…The cordial labeling concept was first introduced by cahit [2]. The quotient-3 cordial labeling have been introduced by P. Sumathi, et al found in [3][4][5][6]. They found some family of graphs are quotient-3 cordial.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy quotient-3 cordial labeling of star related graphs- Paper I

Sumathi¹,

Kumar²

2019

Malaya J. Mat

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Let G(V, E) be a simple, finite and planar graph of order p and size q. In this paper, the concept of Fuzzy Quotient-3 Cordial Labeling was introduced. Let σ : V (G) → [0, 1] be a function defined by σ (v) = r 10 , r ∈ Z 4 − {0}. For each edge uv define µ : E(G) → [0, 1] by µ(uv) = 1 10 3σ (u) σ (v) where σ (u) ≤ σ (v). The function σ is called fuzzy quotient-3 cordial labeling of G if the number of vertices labeled with i and the number of vertices labeled with j differ by at most 1, the number of edges labeled with i and the number of edges labeled with j differ by at most 1 where i, j ∈ r 10 , r ∈ Z 4 − {0} , i = j. The number of vertices having label i denotes v σ (i) and the number of edges having label i denotes e µ (i). Here it is proved that the Star graph and Star related graphs are Fuzzy Quotient-3 Cordial.

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Quotient Labeling of Corona of Ladder Graphs

Abstract: -Let G (V, E) be a finite, non-trivial, simple and undirected graph of order n and size m. For an one to one assignment

Cited by 4 publications

References 2 publications

Grundy number of corona product of some graphs

Grundy number of corona product of some graphs

A Study on C‐Exponential Mean Labeling of Graphs

Fuzzy quotient-3 cordial labeling of star related graphs- Paper I

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