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 … WebSep 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
Strong edge chromatic index of the generalized Petersen graphs ...
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 … WebNot to be confused with Edge coloring. A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In ... nits in the hair
Generalized Petersen graph - HandWiki
If \((P(n, k), \sigma )\) is 3-edge-colorable, then all edges using the color 0 form a perfect matching, denoted by \(M_0\). Furthermore, \((P(n, k), \sigma )-M_0\)is formed of balanced cycles. See more Note that P(n, k) is cubic. If \((P(n, k), \sigma )\) is 3-edge-colorable, then three colors are present at each vertex. It is obvious that all edges colored 0 form a perfect matching, \((P(n, k), \sigma )-M_0\) is a 2-regular graph. … See more For \((P(n, k), \sigma )\) with an arbitrary signature \(\sigma \), let \(\sigma '\in [\sigma ]\) such that \( E^{\sigma '-} \)be as small as possible, … See more If \((P(n, k), \sigma )\) has a perfect matching, denoted by M, and \((P(n, k), \sigma )-M\) is formed of balanced cycles, then \((P(n, k), \sigma )\)is 3-edge-colorable. See more For any perfect matching M of \((P(n, k), \sigma )\), if \((P(n, k), \sigma )-M\) has at least one unbalanced cycle, then \((P(n, k), \sigma )\)is not 3-edge-colorable. See more Web3, all cycle permutation graphs, and all generalized Petersen graphs admit a locally irregular edge-coloring with at most 3 colors. We also discuss when 2 colors su ce for a locally irregular edge-coloring of cubic graphs and present an in nite family of cubic graphs of girth 4 which require 3 colors. Keywords: locally irregular edge-coloring ... WebA 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 Petersen graph with and can be strong … nursing awards