منابع مشابه
Vector Spaces and the Petersen Graph
It is shown that a matching covered graph has an ear decomposition with no more than one double ear if and only if there is no set S of edges such that |S∩A| is even for every alternating circuit A but |S ∩C| is odd for some even circuit C. Two proofs are presented. The first uses vector spaces and the second is constructive. Some applications are also given.
متن کاملAddressing the Petersen graph
Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N -tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observed that N ≥ h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matri...
متن کاملThe ubiquitous Petersen graph
Chartrand, G., H. Hevia and R.J. Wilson, The ubiquitous Petersen graph, Discrete Mathematics 100 (1992) 303-311.
متن کاملSIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL
Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.
متن کاملOn Generalizations of the Petersen Graph and the Coxeter Graph
In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arc-transitive or distance-regular. Girths and odd girths are computed. A problem on hamiltonicity is posed.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/733