Results 271 to 280 of about 2,650,610 (297)

On the nullity of middle graphs

Linear Algebra and its Applications
The nullity of a graph is the multiplicity of \(0\) as an eigenvalue of its adjacency matrix. Classifying connected graphs with a given nullity is a difficult problem. \textit{I. Gutman} and \textit{I. Sciriha} [Discrete Math. 232, No. 1--3, 35--45 (2001; Zbl 0971.05070)] showed that, although the nullity of connected line graphs is unbounded, the case
Xinmei Yuan, Danyi Li, Weigen Yan
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The Prism Over the Middle-levels Graph is Hamiltonian

Order, 2005
Let \textbf{B}\(_k\) be the bipartite graph whose vertices are subsets of size \(k\) or \(k+1\) of the set \(\{1,2,\dots,2k+1\}\), and whose edges represent the inclusion between two such subsets. The authors prove that the prism over \textbf{B}\(_k\) is Hamiltonian and that \textbf{B}\(_k\) has a closed spanning 2-trail.
Peter Horák, Tomás Kaiser, Moshe Rosenfeld 0001, Zdenek Ryjácek   +3 more
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On the toughness of the middle graph of a graph.

Ars Comb., 2001
The middle graph \(M(G)\) of a graph is the graph obtained from \(G\) by inserting a new vertex into every edge of \(G\) and by joining by edges those pairs of these new vertices which lie on adjacent edges of \(G\). Let \(\omega (G-S)\) be the number of connected components of the graph \(G-S\) obtained from a graph \(G\) by deleting a subset \(S\) of
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On the number of perfect matchings of middle graphs

Discrete Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jingchao Lai, Weigen Yan, Xing Feng
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RUPTURE DEGREE AND MIDDLE GRAPHS

2012
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured by various parameters like connectivity, toughness, integrity, tenacity and scattering number.
Odabaş Z.N., Aytaç A.
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Algebraic connectivity of the line graph, the middle graph and the total graph of a regular graph

Ars Comb., 2003
The algebraic connectivity \(a(G)\) of an undirected graph \(G\) is the second smallest eigenvalue of its Laplacian matrix \(L(G)=D(G)-A(G)\), where \(D(G)\) is the diagonal matrix of vertex degrees and \(A(G)\) is the adjacency matrix of \(G\). Let \(\Lambda (G)\), \(M(G)\) and \(T(G)\) denote the line graph, the middle graph and the total graph of a ...
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On characterizations of the middle graphs

TRU Mathematics, 1975
AKIYAMA, JIN, HAMADA, TAKASHI, YOSHIMURA, IZUMI   +2 more
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Graph equations for line graphs, total graphs and middle graphs

TRU Mathematics, 1976
AKIYAMA, JIN, HAMADA, TAKASHI, YOSHIMURA, IZUMI   +2 more
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On the Diameter of Middle Graphs and Total Graphs

International Journal of Mathematics Trends and Technology, 2018
Keerthi G. Mirajkar, Bhagyashri R. Doddamani   +1 more
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FIBONACCI PRIME LABELING OF MIDDLE GRAPHS OF SOME GRAPHS

Graph labeling is a fascinating area of graph theory that assigns integers to the vertices or edges of a graph under specific constraints. In this paper, we focus on Fibonacci Prime labeling, a variant where vertices are assigned distinct Fibonacci numbers such that the labels of adjacent vertices are coprime.
Dr. S. Geethalakshmi, E. Ponemaya
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