منابع مشابه
Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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Hall’s condition for the existence of a proper vertex list-multicoloring of a simple graph G has recently been used to de-ne the fractional Hall and Hall-condition numbers of G, hf(G) and sf(G). Little is known about hf(G), but it is known that sf(G) = max[|V (H)|= (H);H 6G], where ‘6’ means ‘is a subgraph of’ and (H) denotes the vertex independence number of H . Let f(G) and cf(G) denote the f...
متن کاملChromatic polynomials of some nanostars
Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.
متن کاملChromatic Bounds on Orbital Chromatic Roots
Given a group G of automorphisms of a graph Γ, the orbital chromatic polynomial OPΓ,G(x) is the polynomial whose value at a positive integer k is the number of orbits of G on proper k-colorings of Γ. Cameron and Kayibi introduced this polynomial as a means of understanding roots of chromatic polynomials. In this light, they posed a problem asking whether the real roots of the orbital chromatic ...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards
سال: 1954
ISSN: 0091-0635
DOI: 10.6028/jres.052.008