Critical graphs of given diameter
Webof diameter D on n vertices. Observe that C5, the cycle of length 5 and the Petersen graph are critical graphs of diameter 2. Critical graphs have been extensively studied (see … Webthe graph Q-x is e-critical and v-critical and the graph C~ is e-critical but not v-cri- tical. We note that v0-critical graphs are defined in [4] and [8], where some basic properties …
Critical graphs of given diameter
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Webdiameter greater than k if and only if I E' I ~ t. Denote the class of (k,t)-critical graphs by ~(k.t). (k, 1) -cri tical graphs do exist. For example : ~(k, 1) contains the cycle of length … WebDec 1, 2014 · A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty …
WebJul 20, 2014 · A graph is diameter-2-critical if and only if its complement is 3 t-critical or 4 t-supercritical. The 4 t -supercritical graphs are characterized in [ 20 ]. Theorem 3.2 ([ 20 ]). WebDec 1, 1987 · A graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge increased its diameter. We prove that if G is diameter 2-critical graph on n vertices and e edges, then (i) e⩽ [ 1 4 n 2] for n⩽24, and (ii) e< 1 4 n 2 + (n 2 - 16.2n + 56)/320 (<0.2532 n 2 ), for n ⩾25.
WebThe blue lines represent the confidence levels of responses. In each graph, the slope of the line indicates the relationship between the response and the variable. The steeper slope indicates greater dependence. For instance, in the graphs of the first row, EE% is extremely dependent on the polymer/drug ratio. Webthe graph Q-x is e-critical and v-critical and the graph C~ is e-critical but not v-cri- tical. We note that v0-critical graphs are defined in [4] and [8], where some basic properties are given. 2. Simple results. One can verify the following sufficient conditions for a graph to be v-critical. LEMMA 1. Let G be a graph of diameter d>=2 ...
WebAbstract For a connected graph G, the Kirchhoff index is defined as K f ( G ) = ∑ 1 ≤ i < j ≤ n R G ( v i , v j ) and the multiplicative eccentricity resistance-distance index ξ R ∗ ( G ) = ∑ { v i...
WebJan 1, 1979 · A graph G is diameter k-critical if the graph has diameter k and the deletion of any edge increases its diameter. We show that every diameter 2-critical graph on v … download chirotouch installerWebMar 1, 2016 · A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly increases the diameter.In this paper, we prove several results related … clark meaning nameWebMar 1, 1992 · Going critical : an investigation of diameter -critical graphs Joshua Madden Mathematics 1999 We define a graph G = (V, E) with m = \E\ edges, n = \V\ vertices, maximum degree D, and diameter d, to be d-critical if it has the property that for any edge e G E, the graph G — e has diameter > d.… 3 download chipset amd b350WebJan 1, 2013 · If G is a diameter-2 graph, then G is either a star or G has girth 3, 4, or 5. The diameter-2 graphs of girth 5 are precisely the diameter-2 Moore graphs. It is shown (see [143, 185]) that Moore graphs are r-regular and that diameter-2 Moore graphs have order \(n = {r}^{2} + 1\) and exist for r = 2, 3, 7, and possibly 57, but for no other degrees. download chirp audiobooks appWebIn graph theory, the degree diameter problem is the problem of finding the largest possible graph for a given maximum degree and diameter.The Moore bound sets limits on this, … download chirp for baofengWebJ. Plensik, Critical graphs of given diameter, Acta Fac. Rerum Natur. Univ. Comenian. Math. 30 (1975), 71–93. Y. Shang, A remark on the chromatic polynomials of incomparability graphs of posets, Inter- national Journal of Pure and Applied Mathematics, 67 (2) (2011), 159–164. Y. Shang, Lower bounds for the Estrada index of graphs, Electron. J. clark meatsWebJan 1, 2013 · Recall that for graphs G and H, the Cartesian product G H is the graph with vertex set V (G) ×V (H) where two vertices (u 1, v 1) and (u 2, v 2) are adjacent if and only if either u 1 = u 2 and v 1 v 2 ∈ E(H) or v 1 = v 2 and u 1 u 2 ∈ E(G).The most famous open problem involving domination in graphs is the more than four-decade-old conjecture of … download chirp for windows