Edge coloring of generalized petersen graph
WebIn graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star … WebFor integersnandkwith 2 ≤ 2k
Edge coloring of generalized petersen graph
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WebAug 2, 2024 · Every generalized Petersen graph P(n,k) with n > 2k and k 4 can be strong edge colored with at most 9 2, we give some lemmas. In Section3, we show how to color generalized Petersen graphs P(n,k) with n > 2k and k 4 with 9 colors. 2. Lemmas Lemma 1. If P(n,k) is a generalized Petersen graph with n > 2k, k 4 and n = ak + b, then all inner WebJul 15, 2013 · Edge coloring. Generalized Petersen graphs. Total labeling. 1. Introduction. Let be a simple graph with vertex set and edge set . We denote by the …
WebMay 1, 2016 · Various other properties of generalized Petersen graphs have been recently theoretically investigated in the following areas: Hamiltonian property [11], the cop number [12], the total... WebAbstract. A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are adjacent to a common …
WebMar 21, 2024 · A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by . WebMay 19, 2024 · In this paper, we consider the injective edge coloring numbers of generalized Petersen graphs P ( n, 1) and P ( n, 2). We determine the exact values of …
WebMar 15, 2024 · A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are adjacent to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted by χ s ′ (G), is the minimum number of colors needed for a strong edge coloring of G.We …
WebOct 27, 2024 · Star edge-coloring of some special graphs. The star chromatic index of a multigraph , denoted by , is the minimum number of colors needed to properly color the edges of such that no path or cycle of length is bicolored. In this paper, we study the star edge-coloring of Halin graphs, -power graphs and the generalized Petersen graphs . show button for show password in textWebAbstract. A family of graphs which includes the Petersen graph is postulated, and it is conjectured that the Petersen graph is the only member of this family not to have a Tait coloring. A general theorem about Tait colorings is proved and the conjecture is shown to be equivalent to a combinatorial assertion involving cyclically ordered arrays ... show buttonWebOct 5, 2014 · In this paper, we prove that the generalized Petersen graph P (n,k) is acyclically 3-colorable except P (4,1) and the classical Petersen graph P (5,2). 1 Introduction For a graph G, we denote by V (G) and E (G) the set of vertices and edges of G respectively. For a subset V'\subseteq V (G), G [V'] denotes the subgraph of G induced … show butterfly gardensWebOct 4, 2024 · Graph GP (6,1)—edge metric base is colored red (color figure online) Full size image The metric dimension of generalized Petersen graphs GP ( n , k) is studied for different values of k: Case k=1 is concluded in [ 12 ]; Case k=2 is proven in [ … show butteryWebA strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2024, Yang and Wu proposed a conjecture that every generalized... show button top in androidWebAug 2, 2024 · A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2024, … show butterfly haircutWebSep 12, 2024 · The Peterson graph is a cubic graph with 10 vertices and 15 edges. is a unique (3,5)-cage graph and the unique (3,5)-Moore graph. is the odd graph with parameter 3. This is the Kneser graph wherein two vertices are adjacent if and only if the corresponding subsets are disjoint. is also a complement of the line graph k 5 show button shapes