Automorphic chromatic index of generalized Petersen graphs
نویسندگان
چکیده
The automorphic A-chromatic index of a graph Γ is the minimum integer m for which Γ has a proper edge-coloring with m colors which is preserved by a given subgroup A of the full automorphism group of Γ. We compute the automorphic A-chromatic index of each generalized Petersen graph when A is the full automorphism group.
منابع مشابه
Graceful labelings of the generalized Petersen graphs
A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
متن کاملThe lower bound for the number of 1-factors in generalized Petersen graphs
In this paper, we investigate the number of 1-factors of a generalized Petersen graph $P(N,k)$ and get a lower bound for the number of 1-factors of $P(N,k)$ as $k$ is odd, which shows that the number of 1-factors of $P(N,k)$ is exponential in this case and confirms a conjecture due to Lovász and Plummer (Ann. New York Acad. Sci. 576(2006), no. 1, 389-398).
متن کاملDistinguishing and Distinguishing Chromatic Numbers of Generalized Petersen Graphs
Albertson and Collins defined the distinguishing number of a graph to be the smallest number of colors needed to color its vertices so that the coloring is preserved only by the identity automorphism. Collins and Trenk followed by defining the distinguishing chromatic number of a graph to be the smallest size of a coloring that is both proper and distinguishing. We show that, with two exception...
متن کاملDominating -color Number of Generalized Petersen Graphs
Dominating -color number of a graph is defined as the maximum number of color classes which are dominating sets of and is denoted by d, where the maximum is taken over all -coloring of . In this paper, we discussed the dominating -color number of Generalized Petersen Graphs. We have also discussed the condition under which chromatic number equals dominating -color number of Generalized Pet...
متن کاملChromatic 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 کامل