Báo cáo toán học: "A note on constructing large Cayley graphs of given degree and diameter by voltage assignments" pdf

... even larger Cayley graphs based on groups which A note on constructing large Cayley graphs of given degree and diameter by voltage assignments ∗ Ljiljana Brankovi´c, Mirka Miller Department of ... degree/ diameter problem,whichis to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of...

Ngày tải lên: 07/08/2014, 06:22

... 1 For any value of r, the expression ln E as function of (α, β, x, y) ∈Dis convex. The proof of Claim 1 is given in an appendix. Given now that ln E is convex, as a function of (α, β, x, y) ∈Dwe ... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of different p...

Ngày tải lên: 07/08/2014, 06:20

... assumptions of the lemma (and is not a forbidden one), hence we again obtain a contradiction by induction. the electronic journal of combinatorics 15 (2008), #N35 2 3 Main Result For a given total-weighting ... not forbidden and complies with the assumptions of the lemma, hence, by induction, there is an element a j = 0 such that a j−1 + a j+1  3, a contradiction. Therefore, w...

Ngày tải lên: 07/08/2014, 15:22

... u 0 v 0 first. the electronic journal of combinatorics 16 (2009), #N33 2 Proof. By symmetry, we only need consider the case 3k  i  n/2. Let P(u 0 , u i ) be a shortest path between u 0 and u i . Note that ... u l−s to u i along the outer cycle is a shortest path between u 0 and u i , as desired.  In what follows, we give the proof of the main theorem. Proof of Theorem 2: By...

Ngày tải lên: 07/08/2014, 21:21

... Foundation of China (11061012), the project supported by program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011]47), and ... to get stronger results if we use larger weights. And it would be of considerable interest to determine the optimal weights. On the other hand, by the Theorem 1 of Schatte [3]...

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Ngày tải lên: 05/08/2014, 15:21

... Theory of Graphs, Allyn and Bacon, Boston, 1971. Note on Maximal Nonhamiltonian Burkard–Hammer Graphs 399 exists a maximal nonhamiltonian Burkard–Hammer graph G = S(I ∪ K, E) with |I| = m and δ(G)=|I|−k ... Formulations of the Main Results and Discussions By Theorem 2 in the previous section there are no nonhamiltonian Burkard– Hammer graphs G = S(I ∪ K, E)withδ(G) ≥|I|−2...

Ngày tải lên: 06/08/2014, 05:20

... x, y ∈ Σ ∗ , the concatenation of x and y, written xy, is simply the string consisting of x followed by y. The word with no letters is called the empty word and is denoted by . Suppose w ∈ Σ ∗ . ... finite string of letters from Σ. The length of word w is the number of letters in w, denoted by |w|. Thus |banana| = 6, for example. The language consisting of all words over...

Ngày tải lên: 07/08/2014, 06:20