منابع مشابه
The 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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Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
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Let G be a graph on vertices v1,v2, . . . ,vn. The b-chromatic number of G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1≤ i≤ k, has at least one representant xi adjacent to a vertex of every color j, 1 ≤ j 6= i ≤ k. In this paper, we give the exact value for the b-chromatic number of power...
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In this paper we study the chromatic number of the following four flip graphs: A graph on the perfect matchings of the complete graph on 2n vertices and three graphs on the triangulations, Hamiltonian geometric non-crossing paths, and triangles respectively of a point set in convex position in the plane. We give tight bounds for the latter two cases and upper bounds for the first two.
متن کاملSome relations between rank, chromatic number and energy of graphs
The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. Let G be a graph of order n and rank(G) be the rank of the adjacency matrix of G. In this paper we characterize all graphs with E(G) = rank(G). Among other results we show that apart from a few families of graphs, E(G) ≥ 2max(χ(G), n − χ(G)), where n is the number of vertices of G, G ...
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ژورنال
عنوان ژورنال: Malaya Journal of Matematik
سال: 2019
ISSN: 2319-3786,2321-5666
DOI: 10.26637/mjm0s01/0102