Browsing by Author "Erdogan, Fatma Ozen"

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    Independence number of graphs and line graphs of trees by means of omega invariant
    (Springer, 2020-02-26) Srivastava, Gautam; Srivastava, Hari Mohan; Ozden, Hacer; ÖZDEN AYNA, HACER; Zihni, Fikriye Ersoy; Erdogan, Fatma Ozen; ÖZEN ERDOĞAN, FATMA; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; 0000-0002-3991-0488; AAH-5090-2021; ABA-6206-2020; J-3505-2017; AAG-8274-2021
    A recently defined graph invariant denoted by O(G) for a graph G is shown to have several applications in graph theory. This number gives direct information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges, etc. In this paper, we use O to give a characterization of connected unicyclic graphs, to calculate the omega invariant and to formalize the number of faces of the line graph of a tree, and give a new algorithm to formalize the independence number of graphs G and line graphs L(G) by means of the support vertices, pendant vertices and isolated vertices in G.