منابع مشابه
Integral Cayley Multigraphs over Abelian and Hamiltonian Groups
It is shown that a Cayley multigraph over a group G with generating multiset S is integral (i.e., all of its eigenvalues are integers) if S lies in the integral cone over the boolean algebra generated by the normal subgroups of G. The converse holds in the case when G is abelian. This in particular gives an alternative, character-theoretic proof of a theorem of Bridges and Mena (1982). We exten...
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We prove the following conjecture of Bill Jackson ( J. London Math. Soc. (2) 21 (1980) p. 391). If G is a 2-connected multigraph with minimum degree at least 4 and containing no Petersen minor, then G contains a circuit C such that G E(C) is 2-connected. In fact, G has at least two edge-disjoint circuits which can serve as C. Until now, the conjecture had been veri ed only for planar graphs and...
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A graph G is called randomly H − decomposable if every maximal H − packing in G uses all edges in G. G is called H − equipackable if every maximal H − packing in G is also a maximum H − packing in G. M2 − decomposable graphs, randomly M2 − decomposable graphs and M2 − equipackable graphs have been characterized. The definitions could be generalized to multigraphs. And M2 − decomposable multigra...
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ژورنال
عنوان ژورنال: IEEE Transactions on Network Science and Engineering
سال: 2018
ISSN: 2327-4697
DOI: 10.1109/tnse.2017.2730261