scholarly journals ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS

2021 ◽  
Vol 7 (1) ◽  
pp. 38
Author(s):  
Pavel A. Gein
Keyword(s):  
Chromatic Polynomial ◽  
Chromatic Uniqueness ◽  
Tripartite Graphs

Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called chromatically equivalent iff \(P(G, x) = H(G, x)\). A graph \(G\) is called chromatically unique if \(G\simeq H\) for every \(H\) chromatically equivalent to \(G\). In this paper, the chromatic uniqueness of complete tripartite graphs \(K(n_1, n_2, n_3)\) is proved for \(n_1 \geqslant n_2 \geqslant n_3 \geqslant 2\) and \(n_1 - n_3 \leqslant 5\).

scholarly journals Chromatic Polynomial and Chromatic Uniqueness of Necklace Graph

2018 ◽  
Author(s):  
Usman Ali ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Sakina Ashraf
Keyword(s):  
Chromatic Polynomial ◽  
Chromatic Uniqueness ◽  
Necklace Graph

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph Nn, for n ≥ 2 has been determined. It is further shown that N3 is chromatically unique.

scholarly journals A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs

2004 ◽  
Vol 289 (1-3) ◽  
pp. 175-179 ◽  
Author(s):  
Ruying Liu ◽  
Haixing Zhao ◽  
Chengfu Ye
Keyword(s):  
Complete Solution ◽  
Chromatic Uniqueness ◽  
Tripartite Graphs

User opinions driven social recommendation system

2021 ◽  
Vol 25 (1) ◽  
pp. 21-31
Author(s):  
Lakshmikanth Paleti ◽  
P. Radha Krishna ◽  
J.V.R. Murthy
Keyword(s):  
Social Networks ◽  
Collaborative Filtering ◽  
Recommendation System ◽  
Recommendation Systems ◽  
Social Recommendation ◽  
Novel Approach ◽  
Tripartite Graphs ◽  
Content Based Filtering

Recommendation systems provide reliable and relevant recommendations to users and also enable users’ trust on the website. This is achieved by the opinions derived from reviews, feedbacks and preferences provided by the users when the product is purchased or viewed through social networks. This integrates interactions of social networks with recommendation systems which results in the behavior of users and user’s friends. The techniques used so far for recommendation systems are traditional, based on collaborative filtering and content based filtering. This paper provides a novel approach called User-Opinion-Rating (UOR) for building recommendation systems by taking user generated opinions over social networks as a dimension. Two tripartite graphs namely User-Item-Rating and User-Item-Opinion are constructed based on users’ opinion on items along with their ratings. Proposed approach quantifies the opinions of users and results obtained reveal the feasibility.

scholarly journals Diffusion-based recommendation with trust relations on tripartite graphs

2017 ◽  
Vol 2017 (8) ◽  
pp. 083405 ◽  
Author(s):  
Ximeng Wang ◽  
Yun Liu ◽  
Guangquan Zhang ◽  
Fei Xiong ◽  
Jie Lu
Keyword(s):  
Tripartite Graphs

Toroidal polyhexes, tripartite graphs, and double groups

2004 ◽  
Vol 102 (11-12) ◽  
pp. 1231-1241 ◽  
Author(s):  
R. B. King*
Keyword(s):  
Tripartite Graphs

scholarly journals On the nullity of a family of tripartite graphs

2016 ◽  
Vol 8 (1) ◽  
pp. 96-107
Author(s):  
Rashid Farooq ◽  
Mehar Ali Malik ◽  
Qudsia Naureen ◽  
Shariefuddin Pirzada
Keyword(s):  
Adjacency Matrix ◽  
Bipartite Graphs ◽  
Eigenvalue Zero ◽  
Tripartite Graphs ◽  
Graph Form

Abstract The eigenvalues of the adjacency matrix of a graph form the spectrum of the graph. The multiplicity of the eigenvalue zero in the spectrum of a graph is called nullity of the graph. Fan and Qian (2009) obtained the nullity set of n-vertex bipartite graphs and characterized the bipartite graphs with nullity n − 4 and the regular n-vertex bipartite graphs with nullity n − 6. In this paper, we study similar problem for a class of tripartite graphs. As observed the nullity problem in tripartite graphs does not follow as an extension to that of the nullity of bipartite graphs, this makes the study of nullity in tripartite graphs interesting. In this direction, we obtain the nullity set of a class of n-vertex tripartite graphs and characterize these tripartite graphs with nullity n − 4. We also characterize some tripartite graphs with nullity n − 6 in this class.

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