The SVE Method for Regular Graph Isomorphism Identification

Abstract

A regular graph is a type of graph that has particular features. Such graphs have great symmetry, which increases the difficulty of isomorphism identification. In this paper, we propose a new method to address regular graph isomorphism identification. We make some adjustments to the original circuit simulation (CS) method in the graph isomorphism identification process, using single-vertex excitation (SVE) in place of the original excitation, which could remove the confusion of corresponding vertices caused by the graph's symmetry. This new SVE method could widen the range of the application of the original CS method and create better performance in time consumption compared with other traditional methods. The performance of the SVE method is provided in this paper illuminating its practicality and superiority.

Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

“…Step 4: There are two corresponding relations by comparing S 7 a,1 with S 7 b,1,1 and S 7 b,1,2 : b a M 1 = {28, 29, 30, 9, 8, 1, 2, 3, 4, 5, 6, 7, 14, 16, 17, 18, 19, 20, 21, 26, 25, 24, 23, 27, 15, 13, 11, 12, 10, 22}, b a M 2 = {28, 29,30,9,8,1,2,3,4,5,6,7,14,16,17,18,19,20,25,26,21,22,23,27,15,13,11,12, 10, 24}.…”

“…By using this method, the sufficiency of isomorphism detection was obtained based on vertex correspondence. Other isomorphism detection methods, such as partition matching algorithm [13], hybrid immune algorithm [14], optimized circuit simulation [15][16][17], connectivity number and entropy [18], binary code [19], information theory [20], joint matrix [21,22], loop theory [23][24][25][26], high-order adjacency link values [27], are noticeable too. Although all the abovementioned synthesis methods can identify the isomorphism, they cannot accurately find the similar vertices that are beneficial for mechanism selection and isomorphism detection.…”

Detection of slag inclusions using infrared thermal imagining system

“…As for MMA welding on-line quality checking is highly rare, different nondestructive testing (NDT) methods are used after the joining process is completed [10,11]. Most popular are ultrasonic examinations as well as radiographic (X-ray) testing used mainly off-line, but also in some applications and environments in on-line constant monitoring manner [12,13]. Radiographic test results are highly reliable and easier to interpret as the ultrasonic examination results.…”

A joint–joint matrix representation of planar kinematic chains with multiple joints and isomorphism identification

“…There are many other methods. 14,[17][18][19][20] Among them, there are sundry problems, such as complex methods, not intuitive, large calculation workload, and inconvenient to use computer processing. Isomorphism identification has been the focus study of planar kinematic chain synthesis.…”