7789651
The vertex-face total chromatic number of Halin graphs
3006898
A six-color theorem for the edge-face coloring of plane graphs
Abstract It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with Δ ⩽ 3 can be colored by six colors.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
16941824
On the equitable chromatic number of complete n-partite graphs
Abstract In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph Kp1,p2,…,pn. Namely, if M is the largest integer such that p i ( mod M) p i M (i=1,2,…,n) then χ e (K p 1 ,p 2 ,…,p n )= ∑ i=1 n p i M+1 , where χe(G) is the equitable chromatic number of graph G.
37643061
Adjacent strong edge coloring of graphs
Abstract For a graph G ( V , E ), if a proper k -edge coloring ƒ is satisfied with C ( u ) ≠ C ( v ) for uv ∈ E ( G ), where C(u) = {ƒ(uv) | uv ∈ E} , then ƒ is called k-adjacent strong edge coloring of G , is abbreviated k-ASEC , and χ ′ as ( G ) = min { k | k - ASEC of G } is called the adjacent strong edge chromatic number of G . In this paper, we discuss some properties of χ′ as ( G ), and obtain the χ′ as ( G ) of some special graphs and present a conjecture: if G are graphs whose order of each component is at least six, then χ ′ as ( G ) ≤ Δ ( G ) + 2, where Δ( G ) is the maximum degree of G .
14910614
An inequality between the diameter and the inverse dual degree of a tree
Let T be a nontrivial tree with diameter D(T) and radius R(T). Let I(T) be the inverse dual degree of T which is defined to be ΣueV(T) 1/d(u), where d(u) = (Συ∈ N(u)d(υ))/d(u) for u ∈ V(T). For any longest path P of T, denote by a(P) the number of vertices outside P with degree at least 2, b(P) the number of vertices on P with degree at least 3 and distance at least 2 to each of the end-vertices of P, and c(P) the number of vertices adjacent to one of the end-vertices of P and with degree at least 3. In this note we prove that I(T) ≥ D(T)/2+ a(P)/3 + b(P)/10 + c(P)/12 + 5/6. As a corollary we then get {R(T) + 1/3 if D(T) is odd, I(T) ≥ {R(T) + 5/6 if D(T) is even, with equality if and only if T is a path of at least four vertices. The latter inequality strengthens a conjecture made by the program Graffiti.
34732275
Signal extrapolation based on wavelet transform
The Papoulis-Gerchberg (PG) algorithm is used for band-limited signal extrapolation. The PG algorithm is generalized to signals in wavelet subspaces. The generalized PG algorithm is considered for both continuous and discrete time signals. Its convergence is investigated. Numerical examples show its performance.<<ETX>>
32852823
Restricted Edge Connectivity of Edge Transitive Graphs
11343244
Decoupling QoS control from core routers: a novel bandwidth broker architecture for scalable support of guaranteed services
For scalable support of guaranteed services that decouples the QoS control plane from the packet forwarding plane. More specifically, under this architecture, core routers do not maintain any QoS reservation states, whether per-flow or aggregate. Instead, QoS reservation states are stored at and managed by bandwidth broker(s). There are several advantages of such a bandwidth broker architecture. Among others, it relieves core routers of QoS control functions such as admission control and QoS state management, and thus enables a network service provider to introduce new (guaranteed) services without necessarily requiring software/hardware upgrades at core routers. Furthermore, it allows us to design efficient admission control algorithms without incurring any overhead at core routers. The proposed bandwidth broker architecture is designed based on a core stateless virtual time reference system developed in [20].
14083998
Towards CST-enhanced summarization
In this paper, we propose to enhance the process of automatic extractive multi-document text summarization by taking into account cross-document structural relationships as posited in Cross-document Structure Theory (CST). An arbitrary multidocument extract can be CST-enhanced by replacing low-salience sentences with other sentences that increase the total number of CST relationships included in the summary. We show that CST-enhanced summaries outperform their unmodified counterparts using the relative utility evaluation metric. We also show that the effect of a CST relationship on an extract depends on its type.
39930413
A wavelet to DCT progressive image transcoder
A transcoder design is proposed in which the transcoder loads the pre-encoded embedded wavelet coefficients and computes the DCT coefficients. The resulting DCT coefficients are quantized and sorted by multi-grid embedded coding to output a compressed DCT bitstream. This transcoder has two operational modes: open-loop and closed-loop. The open-loop scheme is designed for direct transcoding, targeted to applications in which receivers are connected to the transcoder through a fast network and demand the same rate. In contrast, the closed-loop scheme is designed for fully progressive transcoding, targeted to receivers which are connected to the transcoder through a slow network connection, and may demand heterogeneous rates. The performance of the transcoder is evaluated in both open-loop mode and close-loop mode.