Induced Matching Partition of Petersen and Circulant Graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

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Some star extremal circulant graphs

Discrete Mathematics ◽

10.1016/s0012-365x(02)00872-5 ◽

2003 ◽

Vol 271 (1-3) ◽

pp. 169-177 ◽

Cited By ~ 4

Author(s):

Wensong Lin

Keyword(s):

Circulant Graphs

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Dominating Induced Matching in Some Subclasses of Bipartite Graphs

Theoretical Computer Science ◽

10.1016/j.tcs.2021.06.031 ◽

2021 ◽

Author(s):

B.S. Panda ◽

Juhi Chaudhary

Keyword(s):

Bipartite Graphs ◽

Induced Matching ◽

Dominating Induced Matching

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Hardness results and spectral techniques for combinatorial problems on circulant graphs

Linear Algebra and its Applications ◽

10.1016/s0024-3795(98)10126-x ◽

1998 ◽

Vol 285 (1-3) ◽

pp. 123-142 ◽

Cited By ~ 26

Author(s):

Bruno Codenotti ◽

Ivan Gerace ◽

Sebastiano Vigna

Keyword(s):

Combinatorial Problems ◽

Circulant Graphs ◽

Spectral Techniques

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On the induced matching problem in hamiltonian bipartite graphs

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2090 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Yinglei Song

Keyword(s):

Bipartite Graph ◽

Parameterized Complexity ◽

Bipartite Graphs ◽

Matching Problem ◽

Induced Matching ◽

Subexponential Time ◽

Maximum Induced Matching

Abstract In this paper, we study the parameterized complexity of the induced matching problem in hamiltonian bipartite graphs and the inapproximability of the maximum induced matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian bipartite graph, the induced matching problem is W[1]-hard and cannot be solved in time n o ⁢ ( k ) {n^{o(\sqrt{k})}} , where n is the number of vertices in the graph, unless the 3SAT problem can be solved in subexponential time. In addition, we show that unless NP = P {\operatorname{NP}=\operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of n 1 / 4 - ϵ {n^{1/4-\epsilon}} , where n is the number of vertices in the graph.

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