New concepts of vague graphs

Energy of Bipolar Fuzzy Graphs

“…Let D be a minimum double dominating set of a bipolar fuzzy graph G, then the double dominating energy corresponding to D is defined as an ordered 6 } are double dominating sets of G. The adjacency matrix corresponding to D 1 is calculated as follows:…”

“…Akram et al [3] discussed Laplacian and singless Laplacian energy of bipolar fuzzy graphs and bipolar fuzzy digraphs. For further terminologies and studies on energy of fuzzy graphs and their extensions, readers are referred to [1,2,6,[10][11][12][17][18][19].…”

Certain Concepts of Vague Graphs With Applications to Medical Diagnosis

“…Vague graphs have numerous applications in geometry and operations research and are also useful in many areas of computer science. Rashmanlou and Borzooei [9] studied new concepts relating to vague graphs, product vague graphs [10], regularity of vague graphs [11], and vague competition graphs [12]. Krishna and Lavanya [13] developed new concepts of coloring in vague graphs.…”

“…[9]). A vague graph G is said to be complete if T N (mn) = min(T M (m), T M (n)) and F N (mn) = max(F M (m), F M (n)) for all mn ∈ E.…”

New Concepts of Interval-Valued Fuzzy Graphs with Application

“…Samanta and Pal defined fuzzy tolerance graphs [32], fuzzy threshold graphs [36], fuzzy planar graphs [38], fuzzy k-competition graphs and p-competition fuzzy graphs [34], irregular bipolar fuzzy graphs [35]. Borzooei and Rashmanlou [6][7][8][9][10][11][12] investigated new concepts on vague graphs. In this paper, we present the concepts of neighbourly irregular interval-valued fuzzy graphs, neighbourly totally irregular interval-valued fuzzy graphs, highly irregular interval -valued fuzzy graphs, and highly totally irregular interval-valued fuzzy graphs are introduced and investigated.…”