As a natural generalization of graph coloring, Vince introduced the star chromatic number of a graph G and denoted it by χ∗(G). Later, Zhu called it circular chromatic number and denoted it by χc(G). Let χ(G) be the chromatic number of G. In this paper, it is shown that if the complement of G is non-hamiltonian, then χc(G)=χ(G). Denote by M(G) the Mycielski graph of G. Recursively define Mm(G)=...

A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ(1)(≡<χ(2)> - <χ>(2)) of natural time χ, where = Σp(k)f(χ(k)) and p(k) is the normalized energy released during the kth event of which the natural time is defined as χ(k) = k/N and N stands for the total number of ...

A feasibility study of a 500-GeV linear collider is presented for mSUGRA models in co-annihilation region. We find an active mask is critical to suppress e + e − → e + e − τ + τ − events to probe the models. The grand unification of the three gauge coupling constants arise naturally in minimal SUGRA (mSUGRA) models with universal soft breaking parameters (m 1/2 , m 0 , A 0 , tan β, sign of µ). ...

The standard max chart gives an out-of-control signal when the chart's statistic M exceeds the upper control limit UCL. The probability of M falling below the UCL is given as [3] 2 2 2) UCL (2 2 2) UCL (2 1 2 1 UCL UCL δ χ δ χ δ δ δ δ H H n n , where UCL > 0,) (⋅ Φ is the cumulative distribution function of a standard normal random variable,) (⋅ H is the cumulative distribution function of a ch...

The total chromatic number, χ″(G) is the minimum number of colors which need to be assigned obtain a coloring graph G. Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, χ″(G)≤Δ(G)+2, where Δ(G) represents maximum degree In this paper we obtained some classes four regular circulant graphs.

A search is presented for the direct pair production of a chargino and a neutralino pp → ˜ χ ± 1 ˜ χ 0 2 , where the chargino decays to the lightest neutralino and the W boson, ˜ χ ± 1 → ˜ χ 0 1 (W ± → ± ν), while the neutralino decays to the lightest neutralino and the 125 GeV Higgs boson, ˜ χ 0 2 → ˜ χ 0 1 (h → bb/γ γ // ± νqq). The final states considered for the search have large missing tr...

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of G is denoted by χ′′ a(G). Let mad(G) and ∆(G) denote the maximum average degree and the maximum degree of a graph G, respectivel...