Results 11 to 20 of about 137,715 (267)
On α-adjacency energy of graphs and Zagreb index [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let A(G) be the adjacency matrix and D(G) be the diagonal matrix of the vertex degrees of a simple connected graph G. Nikiforov defined the matrix of the convex combinations of D(G) and A(G) as for If are the eigenvalues of (which we call α-adjacency ...
S. Pirzada +3 more
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The anti-adjacency matrix of a graph: Eccentricity matrix
Discrete Applied Mathematics, 2018 In this paper we introduce a new graph matrix, named the anti-adjacency matrix or eccentricity matrix, which is constructed from the distance matrix of a graph by keeping for each row and each column only the largest distances.
Jianfeng Wang +2 more
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Some New Bounds for α-Adjacency Energy of Graphs
Mathematics, 2023 Let G be a graph with the adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G. Nikiforov first defined the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), 0≤α≤1, which shed new light on A(G) and Q(G)=D(G)+A(G), and yielded some ...
Haixia Zhang, Zhuolin Zhang
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Graceful labeling construction for some special tree graph using adjacency matrix
Electronic Journal of Graph Theory and Applications, 2023 In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)→{0, 1, 2, …, |E(G)|} such that, when each edge uv ∈ E(G) is assigned the label |f(u)−f(v)|
Nikson Simarmata +2 more
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The gamma-Signless Laplacian Adjacency Matrix of Mixed Graphs
Theory and Applications of Graphs, 2023 The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α.
Omar Alomari +2 more
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On the Generalized Adjacency Spread of a Graph
Mathematics, 2023 For a simple finite graph G, the generalized adjacency matrix is defined as Aα(G)=αD(G)+(1−α)A(G),α∈[0,1], where A(G) and D(G) are respectively the adjacency matrix and diagonal matrix of the vertex degrees.
Maryam Baghipur +3 more
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On spectral invariants of the α-mixed adjacency matrix
Discrete Applied MathematicsLet Gˆ be a mixed graph and α∈[0,1]. Let Dˆ(Gˆ) and Aˆ(Gˆ) be the diagonal matrix of vertex degrees and the mixed adjacency matrix of Gˆ, respectively. The α-mixed adjacency matrix of Gˆ is the matrix Aˆα(Gˆ)=αDˆ(Gˆ)+(1−α)Aˆ(Gˆ).We study some properties ...
Lenes, Eber +4 more
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On the mixed adjacency matrix of a mixed graph
, 2016 A mixed graph is a graph with edges and arcs, which can be considered as a hybrid of an undirected graph and a directed graph. In this paper we define the mixed adjacency matrix and the mixed energy of a mixed graph.
Adiga, Chandrashekar +2 more
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Augmented Adjacency Matrix for Topological Configuration of the Metamorphic Mechanisms
Journal of Advanced Mechanical Design, Systems and Manufacturing, 2011 This paper introduces an augmented adjacency matrix with the connectivity of links, the types of joint and its axis-orientation. The configuration transformation matrix for the link-annexing process is presented based on the augmented adjacency matrix ...
Shujun Li, Jian S Dai
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Hermitian adjacency matrix of the second kind for mixed graphs [PDF]
Discrete Mathematics, 2021 This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind introduced by Mohar [21]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u ...
Shuchao Li, Yuantian Yu
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