Abstract
Any number that can be uniquely identified and varied by a graph is known as a graph invariant. This paper will talk about three unique variations of bridge networks, sierpinski networks, honeycomb, and hexagonal networks, with great capability of forecast in the field of software engineering, arithmetic, physics, drug store, informatics, and chemistry in setting with physical and chemical properties. Irregularity sombor invariant is newly introduced and has various expectation characteristics for various variations of bridge graphs or other networks, as mentioned. First, find the irregularities in the networks with the help of the Irregularity sombor index. This will be performed in a step by step procedure. The study will take an existing network, associate it with a graph after finding their vertices and edges, then solve the topology of a graph of a network. Graphical results demonstrate the upper and lower bounds and irregularities of certain networks, and mathematical results are used for modeling purposes. The review settled the topologies of graphs/networks of seven distinct sorts with an Irregularity sombor index. These concluded outcomes can be utilized for the demonstration and modeling of computer networks such as local area networks, Metropolitan area networks, Wide area networks, memory interconnection networks, processor interconnection networks, the spine of the internet, and different networks/designs of Personal computers, power generation networks, mobile base station and chemical compound amalgamation and so on.