Omega invariant of the line graphs of tricyclic

Hacer Özden Ayna


Graphs are probably one of the few fastest growing subjects due to their applications in many areas including Chemistry, Physics, Biology, Anthropology, Finance, Social Sciences, etc. One of the ways of classifying graphs is according to the number of faces. A graph having no cycle is called acyclic, and a graph having one, two, three, faces are respectively called unicyclic, bicyclic, tricyclic. Recently, a new graph invariant denoted by Ω(D) for a realizable degree sequence D is defined. Ω(D) gives a list of information on the realizability, number of faces, components, chords, multiple edges, loops, pendant edges, bridges, cyclicness, connectedness, etc. of the realizations of D and is shown to have several explicit applications in Graph Theory. Acyclic, unicyclic and bicyclic graphs have been studied already in relation with Ω invariant. In this paper, we study tricyclic graphs by means of Ω invariant.

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