On balanced 3-edge product cordial graphs

Graphs have been widely applied in modeling the relationships and structures in real-world applications. Graph construction is the most critical part in these models, while how to construct an effective graph is still an open problem. In this chapter, we propose a novel approach to graph construction based on two observations. First, by virtue of recent advances in low-rank subspace recovery, the similarity between every two samples evaluated in the low-rank code space is more robust than that in the sample space. Second, a sparse and balanced graph can greatly increase the performance of learning tasks, such as label propagation in graph based semi-supervised learning. The k-NN sparsification can provide fast solutions to constructing unbalanced sparse graphs, and b-matching constraint is a necessary route for generating balanced graphs. These observations motivate us to jointly learn the low-rank codes and balanced (or unbalanced) graph simultaneously. In particular, two non-convex models are built by incorporating k-NN constraint and b-matching constraint into the low-rank representation model, respectively. We design a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm to solve the proposed models. Extensive experimental results on four image databases demonstrate the superiority of our graphs over several state-of-the-art graphs in data clustering, transductive and inductive semi-supervised learning.

In this paper we consider the cordiality of a generalized Jahangir graph $J_{n,m}$. We give sufficient condition for $J_{n,m}$ to admit (or not admit) the prime cordial labeling, product cordial labeling and total product cordial labeling.

In this paper we used the cubic roots of unit group together with the concept of cordiality in graph theory to introduce a new method of labeling, this construed cubic cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated and show that the union of any two cycles and the union any two paths are cubic cordial graphs. Also, we study the cubic cordiality for the union of any cycle with a path.

On some operations and density of m-polar fuzzy graphs

In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n ( n≥6 ) and e( G )> n 2 −2n+4 contains a 2-factor with k components, 2 d 1 -cycle, ⋯ , 2 d k -cycle, if one of the following is satisfied: (1) k=2 , δ( G )≥2 and d 1 −2≥ d 2 ≥2 ; (2) k=3 , δ( G )≥ d 3 +2 and d 1 −2≥ d 2 ≥ d 3 ≥4 . In particular, this extends one result of Moon and Moser in 1963 under condition (1).

Distributed robust filtering with [formula omitted] consensus of estimates

A graph is called [see formula in PDF]-extendable if each [see formula in PDF]-matching can be extended to a perfect matching. In this paper, we provide a sufficient condition in terms of the [see formula in PDF]-spectral radius for the [see formula in PDF]-extendability of a connected graph and characterize the corresponding extremal graphs. In addition, such an [see formula in PDF]-spectral condition of a connected balanced bipartite graph is also considered, and the corresponding extremal graphs are determined.

Cordial labeling of hypertrees

We prove that path union of finite copies of helm, closed helm, gear graph are product cordial graphs. Further we prove that the graph obtained by joining two copies of helm by a path of arbitrary length is product cordial graph. We prove similar results for closed helm and gear graph.

Given a bijection \(f:V(G) \rightarrow \{1,2,\cdots ,|V(G)|\}\), we associate two integers \(S=f(u)+f(v)\) and \(D=|f(u)-f(v)|\) with every edge uv in E(G). The labeling f induces an edge labeling \(f':E(G) \rightarrow \{0,1\}\) such that for any edge uv in E(G), \(f'(uv)=1\) if \(gcd(S,D)=1\), and \(f'(uv)=0\) otherwise. Let \(e_{f'}(i)\) be the number of edges labeled with \(i \in \{0,1\}\). We say f is SD-prime cordial labeling if \(|e_{f'}(0)-e_{f'}(1)| \le 1\). Moreover G is SD-prime cordial if it admits SD-prime cordial labeling. In this paper, we investigate some new construction of SD-prime cordial graph.

Scaled Group Consensus over Weakly Connected Structurally Balanced Graphs

Throughout this study we have shown certain graphs such as Z − Pn, subdivision of Z − Pn, braid graph B(n), duplication of leaf node (pendant vertex) by an vertex and by an edge of Z−Pn are difference cordial graphs.

Let G = (V,E) be a graph with p vertices and q edges. A Extended Mean Cordial Labeling of a Graph G with vertex set V is a bijection from V to {0, 1,2} such that each edge uv is assigned the label where ⌈ x ⌉ is the least integer greater than or equal to x with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled with 1 differ by almost 1. The graph that admits an Extended Mean Cordial Labeling is called Extended Mean Cordial Graph. In this paper, we proved that tree related graphs Hdn, K 1,n, Tgn, <K1,n:n> are Extended Mean Cordial Graphs.

In this paper, we investigate some new families of edge sum divisor cordial graphs, face edge sum divisor cordial graphs and total face edge sum divisor cordial graphs.Keywords -Edge sum divisor cordial labelling, Edge sum divisor cordial graph, face edge sum divisor cordial graph, total face edge sum divisor cordial graph, switching of any vertex.

In 2012, Ponraj et al. defined k-product cordial labeling as follows: Let [Formula: see text] be a map from [Formula: see text] to [Formula: see text] where [Formula: see text] is an integer, [Formula: see text]. For each edge [Formula: see text] assign the label [Formula: see text] [Formula: see text]. [Formula: see text] is called a k-product cordial labeling if [Formula: see text], and [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] denote the number of vertices and edges, respectively, labeled with [Formula: see text] [Formula: see text]. A graph that admits k-product cordial labeling is called k-product cordial graph. Later, we proved that several families of graphs are k-product cordial graphs. In this paper, we show that the product of graphs admit k-product cordial labeling.